F-NGIN. 
LIBRARY 


PC-NRLF 


111    D71 


rjigmeering 


EMPIRICAL  DESIGN 


BY 


LESLIE  D.  HAYES,  M.  E. 

Professor  of  Machine  Design  and  Construction, 

West  Virginia  University. 
Member  American  Society  of  Mechanical  Engineers. 


1921 

CORNELL  CO-OPERATIVE  SOCIETY 
ITHACA,  N.  y. 


o  ,,  H 


J^ibrary 


Copyright    1915 
By  CARPENTER  &  CO. 

Copyright    1921 
By     LESLIE  D.    HAYES 
Morgantown,    W.  Va. 


CONTENTS 


CHAPTER  I 

EMPIRICAL  DESIGN 5 

Definition;  Empirical  Methods  in  Modern  Design;  Method 
of  Application;  Empirical  Equations. 

CHAPTER  II 

SCREW  FASTENINGS 11 

General  Forms;  Forms  of  Threads;  Bolts;  Nut  Locks; 
Washers;  Screws  for  Metal;  Screws  for  Wood. 

CHAPTER  IH 

KEYS  AND  TAPER  PINS 25 

Use  of  Keys;  Forms  and  Proportions  for  Keys;  Woodruff 
System  of  Keys;  Keyways  or  Key  Seats;  Taper  Pins. 

CHAPTER  IV 

SHAFTING  AND  SHAFT  FITTINGS 33 

Shafting;  Keyways;  Couplings;  Permanent  Couplings; 
Clutch  Couplings;  Collars. 

CHAPTER  V 

SHAFT  FIXTURES 46 

General  Nature;  Purpose  and  Qualities  of  Bearings;  Forms 
of  Bearings;  Adjustments  of  Bearings;  Proportions  for 
Babbitted  Bearings;  Quarter-box  Bearings;  Bearing  Sup- 
ports; Stands  and  Base  Plates;  Wall  Brackets;  Wall  Box 
Frames;  Hangers. 


793267 


2  CONTENTS 

CHAPTER  VI 

TRANSMISSION  MEMBERS 62 

General  Statements;  Pulleys;  Belts;  Handwheels;  General 
Nature  and  Properties  of  Gears;  Proportions  and  Proper- 
ties of  Gear  Teeth;  Materials  used  in  Gears;  Proportions 
for  Spur  Gears;  Proportions  for  Bevel  Gears;  Proportions 
for  Worm  Gears ;  Commercial  Gears ;  Cams. 

CHAPTER  VH 

PIPE  AND  PIPE  FITTINGS 79 

Varieties  of  Pipe;  Wrought  Iron  and  Steel  Pipe;  Pipe 
Threads;  Pipe  Joints;  Couplings;  Pipe  Flanges;  Pipe 
Bends;  Pipe  Fittings;  Valves. 

DECIMAL  EQUIVALENTS 95 

TRIGONOMETRIC  FUNCTIONS 96 

INDEX. .  101 


PREFACE. 


This  book  has  been  planned  especially  to  meet  the  needs  of  the 
second  year  students  in  the  Department  of  Machine  Design  of 
Cornell  University.  It  is  hoped,  however,  that  the  material  is  of  a 
nature  and  the  arrangement  such  as  to  meet,  in  a  fair  degree,  the 
needs  of  other  technical  schools  and  colleges  for  a  course  in  design 
to  follow  the  elementary  Mechanical  Drawing  and  Descriptive 
Geometry  before  the  student  has  had  the  necessary  preparation  in 
Mechanics  for  a  course  in  theoretical  design. 

It  is  intended  to  give  in  a  convenient  form  such  tables,  formulas 
and  curves  for  the  empirical  proportioning  of  machine  parts  as  are 
necessary  in  a  brief  course  in  Empirical  Design,  and  such  instruc- 
tion as  to  the  methods  of  their  derivation  and  use  that  the  student, 
upon  the  completion  of  the  course,  may  be  able  to  use  material  of 
this  nature  understandingly  and  to  derive  new  material  if  he  so 
desires.  The  data  have  been  collected  at  different  times  and  have 
been  in  use  in  teaching  this  course  in  Cornell  University  for  a 
considerable  period.  The  purpose  and  manner  of  using  the  various 
machine  parts  is  explained  in  detail  for  the  benefit  of  those  students 
whose  previous  training  has  left  them  wholly  unfamiliar  with 
machinery.  In  the  descriptions  and  explanations  a  fair  knowledge 
of  the  principles  of  Mechanical  Drawing,  Descriptive  Geometry 
and  Analytical  Geometry  has  been  assumed. 

No  attempt  has  been  made  to  intrude  upon  the  field  of  the 
engineer's  handbook  but  the  proportions  have  been  carefully  com- 
piled with  the  intent  that  any  here  given  shall  be  reliable  within 
the  limits  of  good  design,  and  some  of  the  more  commonly  used 
mathematical  tables  have  been  added  with  a  view  to  making  it  a 
desirable  book  for  reference  in  the  more  advanced  classes  in 
Machine  Design. 

Acknowledgment  is  due  to  Professors  E.  H.  Wood  and  C.  D. 
Albert  and  to  Mr.  L.  J.  Bradford  for  suggestions  and  criticisms. 
The  author  is  indebted  to  Professor  Wood  for  the  use  of  the  pro- 
portions derived  by  him  for  many  of  the  machine  parts  described, 
and  several  manufacturers  have  responded  freely  to  requests  for 
information. 

June,  1915.  L.  D.  H. 


CHAPTER  I. 


EMPIRICAL  DESIGN 

1.  Definition. — When  a  machine  part  has  been  proportioned 
from  experience  obtained  in  making  other  similar  machine  parts 
and  without  any  direct  application  of  the  theory  and  principles  of 
rational  machine  design  it  is  said  to  have  been  designed  empirically. 
Before  the  principles  and  laws  which  make  modern  design  a  fairly 
exact  science  had  been  discovered  all  design  was  of  an  empirical 
nature,  differing  little  from  guess  work  at  first  but  becoming  more 
and  more  exact  as  the  result  of  increasing  experience,  and  the 
elimination  of  such  designs  as  were  found  to  be  too  weak  or  too 
expensive  in  either  material  or  labor. 

2.  Empirical  Methods  in  Modern  Design. — With  the  discovery 
of  the  laws  governing  the  design  of  a  machine  part  empirical 
methods  of  design  were  usually  superseded.     Sometimes  this  in- 
volved considerable  change  in  the  earlier  designs  but  more  often 
there  was  little  change.    It  would  seem,  then,  that  continued  study 
of  these  principles  and  laws  must  entirely  displace  empirical  meth- 
ods of  design.   There  are,  however,  two  classes  of  parts  in  the  design 
of  which  empirical  methods  are  likely  to  continue,  e.  g.,  those  parts 
of  such  complex  form  that  it  is  very  difficult,  if  not  impossible,  to 
discover  and  apply  the  principles  involved,  and  that  large  class  of 
parts  in  use  in  so  many  sizes  of  similar  proportions  that,  although 
rational  methods  may  have  been  used  in  the  design  of  the  extreme 
sizes,  the  intermediate  sizes  are  much  more  cheaply  designed  by 
empirical  means  based  upon  the  proportions  for  the  extreme  sizes. 
The  discussion  of  the  first  of  these  two  classes  is  beyond  the  scope 
of  this  book  but  an  attempt  will  be  made  to  discuss  some  of  the 
parts  falling  within  this  second  class  and  to  study  the  empirical 
methods  used. 

3.  Method  of  Application. — The  machine  parts  to  which  empiri- 
cal methods  will  be  applied  belong  to  a  large  class  of  parts  in  such 

5 


<5;r  EMPIRICAL  DESIGN 

general  use  under  such  similar  conditions  that  they  are  now  made 
in  a  number  of  standard  sizes  having  the  same  general  form  and 
proportions  and  purchasable  in  the  open  market  at  a  cost  much 
less  than  that  at  which  they  could  be  designed  and  built  especially 
for  each  case.  Empirical  methods  are  also  often  applied  by  manu- 
facturers in  the  design  of  parts  which  they  have  occasion  to  make 
in  a  number  of  sizes  even  though  those  parts  are  never  placed 
upon  the  market  except  in  conjunction  with  some  complete  ma- 
chine. 

Any  of  these  machine  parts  of  modern  origin  have  usually  had 
their  dimensions  for  a  large  and  a  small  size  determined  by  the 
principles  of  rational  machine  design,  while  the  dimensions  for 
parts  of  older  origin  may  have  been  determined  empirically.  In 
either  case  the  corresponding  dimensions  for  the  intermediate  sizes, 
and  sometimes  for  a  small  range  beyond  the  selected  extreme  sizes, 
are  determined  according  to  some  chosen  law  of  variation.  This 
may  usually  be  done  most  conveniently  by  graphical  methods. 

To  make  a  graphical  determination  of  this  kind  the  nominal  sizes 
(by  nominal  size  is  meant  that  dimension  which  gives  name  to  the 
size,  as  the  outside  diameter  in  the  case  of  a  handwheel),  for  the 
range  through  which  it  is  desired  to  construct  the  part,  are  laid  off 
to  any  convenient  scale  of  abscissas  and  ordinates  erected  at  these 
points.  On  the  ordinates  corresponding  to  the  two  sizes,  usually 
near  the  limits  of  the  desired  range,  for  which  all  the  dimensions  are 
known  (having  been  previously  determined  either  by  rational  or  by 
empirical  methods)  the  values  of  these  dimensions  are  laid  off  to 
scale.  This  scale  should  be  so  chosen  that  the  dimensions  may  be 
read  easily  to  as  small  a  fraction  of  an  inch  as  it  is  desirable  to  work 
in  manufacturing  the  part.  What  the  value  of  this  fraction  shall 
be  is  a  matter  for  the  judgment  of  the  draftsman.  His  decision 
must  be  largely  influenced  by  the  size  of  the  part,  whether  it  is  to  be 
left  in  the  rough  or  to  be  machined  to  size  and,  if  it  is  to  fit  some 
other  part,  the  nature  of  the  fit  required.  Its  value  is  rarely 
smaller  than  a  sixteenth  of  an  inch  in  unfinished  castings,  unless 
they  are  very  small,  and  may  often  be  as  great  as  a  fourth  inch  or  a 
half  inch  in  large  castings.  Having  assumed  the  law  of  variations 
for  one  of  these  dimensions  a  curve  following  that  law  is  drawn 
through  the  two  points  already  determined  for  that  dimension. 


EMPIRICAL  DESIGN  7 

The  intersections  of  this  curve  with  each  of  the  remaining  ordinates 
gives  the  value  of  this  dimension  for  the  corresponding  sizes  of  the 
part  to  the  same  scale  as  that  to  which  the  known  values  were  laid 
off. 

As  an  example,  in  the  handwheel,  Fig.  1,  let  it  be  required  to  find 
the  sizes  of  shafts  (dimension  B)  suitable  to  use  with  a  series  of 


FIG.  1 
nominal  sizes  (dimension  A)  when  these  dimensions  are  known  to 

4 


12  16 

•Diameter  of  Handwheel 

FIG.  2 


2O 


24 


be  f"  and  lj"for  the  6"  and  16"  wheels  respectively,  and  the 
variation  assumed  to  be  by  direct  proportion.     On  the  base  line, 


8  EMPIRICAL  DESIGN 

Fig.  2,  lay  off  the  nominal  sizes  and  on  the  ordinates  corresponding 
to  the  6"  and  16"  sizes  lay  off  to  scale  f "  and  1|"  locating  points 
a  and  b  respectively.  The  straight  line  through  these  points 
represents  the  law  of  variation  and  by  its  intersection  with  the 
several  ordinates  determines  the  required  shaft  diameter,  as  1" 
for  the  12"  wheel.  In  the  same  way  the  line  through  points  c  and  d 
determines  the  corresponding  values  for  the  diameters  of  hubs  for 
these  handwheels. 

These  curves  may  be  left  in  their  present  form  for  the  values  to 
be  read  off  when  needed,  the  equations  of  the  curves  may  be  written 
and  the  values  for  the  dimensions  ascertained  by  substitutions  in 
these  equations,  or  the  values  for  the  dimensions  for  all  sizes  that 
it  is  desirable  to  manufacture  may  be  read  off  from  the  curve  at 
once  and  tabulated  for  use.  Of  these  three  methods  the  latter  is 
the  most  convenient  for  general  drafting  room  use  while  the  first 
two  have  the  advantage  of  showing  clearly  the  relation  between  the 
several  dimensions  of  the  machine  part. 

4.  Empirical  Equations. — The  equations  have  an  advantage 
when  compactness  is  a  desirable  quality  and  they  may  also  be 
readily  combined  to  show  the  relation  between  any  two  dimensions, 
whereas  the  curves  refer  all  dimensions  to  the  nominal  size.  For 
these  reasons  the  equation  method  will  be  used  quite  largely  in 
this  book. 

Applying  the  slope  form,  y  =  mx  +  b,  of  the  equation  for  a 
straight  line,  to  the  curves  of  Fig.  2,  and  using  the  symbols  of  Fig.  1, 
gives 

B  =  A  A  +  \"  (1). 

and      C  =   |  A  +  J"     (2). 

As  the  diameter  of  the  hub  is  more  naturally  a  function  of  the 
diameter  of  the  shaft  than  of  the  outside  diameter  of  the  hand- 
wheel,  equations  (1)  and  (2)  may  be  combined  to  eliminate  A 
giving 

C  =  2B (3). 

When  the  variation  desired  for  the  dimensions  of  intermediate 
sizes  does  not  conform  to  the  straight  line  construction  given  above 
the  careful  design  of  one  or  two  additional  sizes  will  readily  locate  a 
suitable  curve  on  the  graphical  construction,  but  it  may  beneces 


EMPIRICAL  DESIGN  9 

sary  to  resort  to  some  of  the  less  simple  methods  of  mathematics 
or  to  the  use  of  logarithmic  cross-section  paper  to  obtain  an  equa- 
tion for  that  curve.  As  these  methods  of  determination  permit 
considerable  variation  in  the  values  taken  for  the  dimensions  it  is 
often  sufficiently  accurate  and  much  easier  to  approximate  the 
curve  by  two  straight  lines  as  illustrated  in  Fig.  3,  where  the  curve 
B  represents  the  selected  law  of  variation  for  the  thickness  of 
babbitt  in  a  certain  type  of  bearing,  in  proportion  to  the  diameter, 

1 


FIG.  3 

A,  of  the  shaft.  The  straight  line  (1)  whose  equation  is  ^  A  +  J  ", 
conforms  closely  to  the  curve  for  diameters  from  4"  to  16",  which 
includes  the  sizes  most  commonly  used,  while  the  straight  line  (2), 
whose  equation  is  j3^  A  +  f",  conforms  well  for  the  smaller  diame- 
ters. We  may,  then,  write 

B  =  4xo  A  +  \"  but  not  to  exceed  A  A  +  J" 


FIG.  4 

as  fairly  representative  of  the  desired  variation  for  the  babbitt 
thickness  for  bearings  of  this  type. 

Many  of  the  dimensions  of  a  machine  part  are  made  up  in  a 


10  EMPIRICAL  DESIGN 

rational  manner  by  adding  together  several  other  dimensions,  the 
values  of  any  or  all  of  which  may  be  of  purely  empirical  origin. 
An  illustration  of  this  occurs  in  the*  diameter,  B,  for  the  flange 
which  procects  the  head  of  the  set  screw  in  the  safety  collar,  shown 
in  Fig.  4.  It  is  made  up  by  adding  to  the  diameter,  A,  of  the  bore 
for  the  shaft,  twice  the  over  all  length  of  the  set  screw.  This 
latter  is,  however,  made  up  of  the  length,  L,  of  the  screw,  measured 
from  the  tip  of  the  point  to  the  under  side  of  the  head,  plus  the 
thickness  of  the  head  which,  in  this  particular  form,  is  empirically 
taken  to  be  one-half  the  diameter.  We  may,  then,  write 
B  =  A  +  2  (L  +  Jd) 
=  A  +  2  L  +  d. 


CHAPTER    II. 


SCREW  FASTENINGS. 

5.  General  Forms. — Screw  fastenings  are  in  use  in  so  many 
ways  that,  besides  the  general  standard  forms  which  are  common 
to  all  lines,  there  have  been  developed  numerous  forms  which  are 
standard  for  special  classes  of  work  and  are  carried  in  stock  in 
regular  sizes  by  the  manufacturers.  In  this  book  the  description 
will  be  confined  to  a  few  of  those  common  forms  which  are  carried 
in  stock  not  only  by  the  manufacturers  but  by  most  dealers  in 
hardware  or  engineering  supplies. 

The  proportions  of  these  fastenings  are  empirical  and,  for  some 
of  them,  the  products  of  all  makers  do  not  agree  in  every  particu- 
lar, but  they  are  in  so  close  general  agreement  that  for  the  same 
stock  form  most  of  them  are  interchangeable.  Such  fastenings 
are  called  for  in  the  bill  of  material  only,  and  no  drawings  made. 
If,  however,  any  variation  is  made  from  the  proportions  for  the 
stock  form  it  becomes  a  "special"  and  a  detail  drawing  must  be 
made.  Specials  greatly  increase  the  cost  and  should  be  avoided 
wherever  it  is  possible  to  use  a  standard  form. 

The  standard  screw  fastenings  are  divided  into  two  general 
classes,  namely,  bolts  and  screws.  In  some  of  their  forms  the 
characteristics  of  the  two  so  overlap  that  there  is  no  clear  distinc- 
tion in  their  nomenclature.  It  is,  perhaps,  simplest  for  the  student 
to  learn  the  class  name  in  conjunction  with  the  form  name  for  each 
case  as  he  meets  it. 


Standard  V  Thread, 
(a) 


FIG.  5. 
11 


U.  S.  Standard  Thread. 
(*) 


12  SCREW  FASTENINGS 

6.  Forms  of   Threads.— While  a  number  of  different  forms  of 
screw  threads  have  been  devised,  the  full  V,  Fig.  5  (a),  and  the 
United  States  Standard  (also  known  as  the  "Sellers"  and  as  the 
"Franklin    Institute"),    Fig.    5(b),    are   used   practically   to   the 
exclusion  of  all  others  for  screw  fastenings  in  the  United  States. 
The  United  States  Standard  form,  being  only  three-fourths  as  deep 
and  with  no  sharp  angle  at  the  root  of  the  threads,  does  not  weaken 
the  bolt  nearly  as  much  nor  is  it  as  easily  multilated  as  the  full  V 
thread.     For  these  reasons  it  is  generally  preferred  and  is  usually 
supplied  by  makers  or  dealers  unless  otherwise  specified. 

7.  Bolts. — The  usual  form  for  a  bolt  has  a  head  at  one  end  with 
a  nut  which  turns  upon  the  threaded  portion  at  the  other  end. 
Either  the  head  or  the  nut  may  be  omitted  or  replaced,  in  some  of 
the  forms.     Bolts  are  used  to  hold  members  together  in  two  distinct 
ways.     They  may  be  used  to  draw  them  together  by  tension 
between  the  head  and  nut  or  they  may  be  passed  through  them  as 
a  pin  or  dowel,  to  prevent  their  sliding  over  each  other,  the  nut 
and  head  serving  to  keep  the  bolt  in  place.     In  the  former  case  it 
is  not  necessary  that  the  holes  should  be  finished  or  fit  the  bolt  but 
in  the  latter  case  the  bolt  and  holes  must  be  machined  to  fit  closely. 
In  either  case  there  should  be  a  good  bearing  surface  under  head 
and  nut  and  in  the  better  class  of  work  such  surfaces  should  be 
machined.     Wherever  the  nature  of  the  work  will  not  permit  of  a 
suitable  bearing  surface  on  the  piece  itself  washers  should  be  used. 
For  further  information  regarding  the  use  of  washers  see  Art.  9, 
page  18. 

The  types  of  bolts  which  we  shall  discuss  are  illustrated  in  Fig. 6 
and  the  numerical  values  of  their  dimensions,  for  diameters  up  to 
3|",  are  given  in  Table  I.  The  relations  between  these  dimensions 
are  expressed  in  the  following  empirical  equations. 


T.P.I.   = 


0.24  \/  D    +   0.625   —  0.175 

1.29904. 

d=D-      T^L 

F  =   li  D  +  J"  rough,  iV'  less  when  finished. 
C  =   1.155  F. 


SCREW  FASTENINGS 


13 


C'  =   1.414  F. 

T    =    D. 

T'  =  }  D  to  D. 

The  length  of  a  bolt,  L,  is  measured  between  the  points  indicated 
in  the  figure,  while  the  length  of  the  perfect  thread  on  the  portion 
threaded  to  receive  a  nut  is  S  =  lj  D;  and  to  enter  a  tapped  hole 
in  a  machine  member  isZ  =  J  S  =  1A  D.  The  hole  into  which 
this  threaded  portion,  Z,  enters  should  have  a  depth  of  perfect 
thread,  X  =  1JS  =  liilX  Forms  such  as  the  machine  bolt  and 


Machine  Bolt. 
(a) 


Tap  Bolt. 

to 

FIG.  6. 


stud  bolt  are  frequently  designated  as  "through  bolts"  to  distin- 
guish them  from  the  tap  bolt  and  stud  which  are  threaded  into  a 
machine  member. 

Bolts  with  hexagon  nuts  cost  about  10%  more  than  those  with 
square  nuts.  When  both  nuts  and  heads  are  hexagonal  the  cost 
is  about  20%  more  than  for  square  heads  and  nuts.  Because  of 
their  greater  cost  boles  having  hexagonal  heads  and  nuts  are  used 
only  when  space  is  lacking,  either  to  allow  the  corners  of  the  nut 
to  pass  or  to  permit  sufficient  wrench  movement  for  a  square  nut; 
or  where  a  more  finished  appearance  is  desirable. 

(a)  Machine  Bolts. — The  stock  form  of  machine  bolts,  Fig. 
6 (a),  have  United  States  Standard  thread  with  standard  hexagonal 
or  square  head  and  standard  hexagonal  or  square  nut.  Lengths 
vary  by  \"  from  Ij"  to  8'' ',  and  by  I"  from  8"  to  30";  diameters 


14  SCREW  FASTENINGS 

TABLE  I. 
U.  S.  STANDARD  SCREW  THREADS,  NUTS  AND  BOLT  HEADS. 


n 
*$ 


T.  P.  I. 
20 
18 
16 
14 
13 

12 

11 

10 

9 

8 

7 
7 
6 
6 


0.185 
0.240 
0.294 
0.344 
0.400 

0.454 
0.507 
0.620 
0.731 
0.837 

0.940 
1.065 
1.160 
1.284 
1.389 

1.490 
1.615 
1.712 
1.962 
2.176 

2.426 
2.629 
2.879 
3.100 


0.027 
0.045 
0.068 
0.093 
0.126 

0.162 
0.202 
0.302 
0.420 
0.550 

0.694 
0.893 
1.057 
1.295 
1.515 

1.744 
2.049 
2.302 
3.023 
3.719 

4.620 
5.428 
6.510 

7.548 


Diagonal  of 
Head  or  Nut. 


& 


*  Rarely  carried  in  stock  by  dealers. 

from  \"  to  2  are  available.     A  bill  cf  material  should  specify  the 
diameter,  length,  head  and  nut. 

(b)  Coupling  Bolts. — Coupling  bolts  differ  from  machine  bolts 
in  that  the  bodies  of  the  bolts  are  milled  to  exactly  fit  reamed  holes 
of  the  same  nominal  diameter  as  the  bolts,  and  the  heads  and  nuts 
are  faced  perpendicular  to  the  axis  of  the  bolt.  Stock  forms  have 
hexagonal  heads  and  nuts  only.  The  diameters  run  from  \"  up 
to  1J",  varying  by  \" ,  and  lengths  from  2"  up  to  6",  varying  by 
1".  Specify  diameter  and  length  in  the  bill  of  material. 


SCREW  FASTENINGS  15 

(c)  Tap  Bolts. — Tap  bolts,  Fig.  6(b),are  sometimes  used  instead 
of  machine  bolts  where  the  work  is  of  such  a  nature  that  the  bolt 
cannot  pass  through  to  receive  the  nut.     The  threaded  end  of  the 
bolt  enters  a  portion  of  the  work  itself  which  serves  as  a  nut. 
Wherever  the  work  requires  frequent  disconnecting  a  stud  is  to  be 
preferred.     Tap  bolts  are   carried  in  stock  with    United   States 
Standard  thread  and  standard  hexagonal  or  square  heads.     Stock 
diameters  run  from  J"  to  I"  and  lengths  from  Ij"  to  4".     Specify 
diameter,  length  and  head  in  a  bill  of  material. 

(d)  Studs. — Studs,  Fig.  6(c),  serve  a  similar  purpose  and  in 
general  are  to  be  preferred  to  tap  bolts.     This  is  especially  true  if 
the  work  has  to  be  disconnected  frequently.     That  portion  of  the 
work  which  receives  the  threaded  end  of  the  stud  serves  as  a  head 
while  the  portion  of  the  work  through  which  the  stud  passes  is  held 
in  place  by  the  nut.     The  stud  remains  permanently  in  place,  and 
wear  on  the  threads  in  a  principal  member  is  avoided.     The  stock 
form  has  United  States  Standard  thread  and  standard  hexagonal  or 
square  nut.     Stock  diameters  run  from  f "  to  1J"  and  lengths  from 
li"  to  10".     Specify  the  diameter,  length  and  nut  in  a  bill  of 
material. 

(e)  Stud  Bolts. — Stud  bolts  differ  from  studs  in  that  both  ends 
are  alike  and  are  fitted  with  a  nut  on  each.     They  are  used  instead 
of  machine  bolts  when  projecting  portions  of  the  material  so  cover 
the  bolt  hole  that  the  bolt  could  be  inserted  only  by  passing  the  bolt 
head  through  the  bolt  hole.     The  second  nut  acts  as  a  detachable 
head.     Bolts  of  extreme  length  are  made  in  this  form  as  it  is  easier 
to  thread  the  end  of  a  long  rod  than  to  forge  a  head  on  it.     The 
stock  forms  and  specifications  are  the  same  as  for  studs. 

(f)  Automobile  Bolts. — The  foregoing  forms  of  bolts  do  not  ful- 
fill  the  exacting  requirements   of  strength  and  space  limits  de- 
manded in  automobile  work.     The  ever  increasing  use  of  automo- 
biles and  the  necessity  for  interchangeability  in  bolts  and  screws 
likely  to  be  broken  or  lost  has  led  to  the  adoption  of  a  special  stand- 
ard for  such  parts  by  the  Society  of  Automobile  Engineers.     Their 
standard  bolts  have  hexagonal  heads  and  nuts  and  United  States 
Standard  thread  but  differ  from  the  usual  form  in  several  points, 
such  as  finer  threads,  smaller  heads   and  nuts,  heads  slotted  for 


16 


SCREW  FASTENINGS 


screw-driver,  end  of  bolts  drilled  and  nuts  recessed  to  lock  with 
cotter  pins,  and  shoulder  on  face  of  heads  and  nuts  to  prevent 
contact  of  corners  while  being  screwed  up.  The  body  of  the  bolt 
is  finished  to  D— 0.001",  and  S  =  If  D.  These  forms  are  illus- 
trated in  Fig.  7  and  the  numerical  values  of  the  dimensions  for 
the  stock  sizes  are  given  in  Table  II. 


HD-O.OOlh- 


Head. 
(a) 


h— F-H^ 


Plain  Nut. 
<*) 


FIG.  7. 
TABLE   II. 
S.  A.  E.  STANDARD  SCREWS  AND  NUTS. 


T.P.I, 

28 

24 

24 

20 

20 

18 
18 
16 
16 
14 

14 
12 
12 
12 
12 


Thickness. 


i 


T, 


M 

I 
1 

\P 

H 


Depth  of  Slots- 


i 

i  i 


E, 


A 


T\ 


Width  of  Slots 


i 

A 

A 
A 


G 

S 

II 
13 


SCREW  FASTENINGS 


17 


8.  Nut  Locks. — Wherever  bolts  on  structures  or  machinery  are 
subjected  to  jarring  or  vibration  there  is  a  tendency  for  the  nuts 
to  work  loose  and  come  off.  This  is  especially  true  where  the 
nature  of  the  work  does  not  permit  the  nut  to  be  set  up  hard  to 
get  the  full  advantage  of  frictional  resistance.  In  such  cases  it  is 
necessary  to  provide  some  form  of  nut  lock.  There  are  a  large 
number  of  different  forms  of  lock  nuts  in  use.  These  vary  widely 
in  complexity  and  costliness.  Three  only  of  the  more  common 
forms  will  be  discussed  here. 

(a)  Jam  Nuts. — Probably  the  commonest  form  of  nut  lock  is 
that  shown  in  Fig.  8  (a).  A  second  nut  is  placed  on  the  bolt  and 
screwed  up  hard  against  the  first  to  prevent  it  from  turning.  It  is 
not  necessary  that  both  of  these  nuts  shall  be  of  standard  thickness 


FIG.  8. 

and  some  controversy  has  arisen  as  to  which  should  be  reduced. 
A  study  of  the  theory  in  each  case  will  reveal  evidence  in  support 
of  both  methods  but  in  general  the  load  is  carried  by  the  outer  nut 
when  fully  set  up.  If  T  =  D  then  T,  =  J  D  to  D  is  permissible. 

(b)  Castellated  Nuts. — The  outer  end  of  this  form  of  nut  is 
prolonged  and  through  this  cylindrical  prolongation  diametrical 
slots  are  milled  as  illustrated  in  Fig.  7(c).  A  hole  drilled  diamet- 
rically through  the  end  of  the  bolt  permits  a  split  cotter  pin  to  be 
passed  through  the  bolt  wth  its  ends  projecting  into  the  slot  on 
either  side,  thus  providing  a  positive  lock  to  the  nut.  The  ad- 
vantage of  the  positive  locking  is  overcome  for  some  purposes  by 
the  necessity  of  turning  through  60°  between  the  successive  locking 
positions.  In  the  discussion  of  automobile  bolts  in  the  preceding 
article  mention  was  made  of  a  provision  for  locking  the  nut  by 
means  of  a  cotter  pin.  This  is  perhaps  the  most  common  appli- 


18  SCREW  FASTENINGS 

cation  of  the  castellated  nut.  The  stock  sizes  correspond  to  the 
sizes  of  automobile  bolts  given  in  Table  II  on  page  16  and  they  are 
obtainable  either  soft  or  casehardened. 

(c)  Marine  Nut  Lock. — The  marine  nut  lock  requires  a  special 
form  of  nut  with  a  cylindrical  projection  on  the  under  side  ex- 
tending through  a  separate  locking  ring,  as  shown  in  Fig.  8(b). 
The  locking  ring  is  prevented  from  turning  by  a  pin  set  in  the  ad- 
jacent member  and  a  set  screw  in  the  ring  is  clamped  against  the 
projection  on  the  nut  to  secure  it.  A  groove  is  cut  in  this  pro- 
jection to  prevent  any  burr  caused  by  the  cup  point  of  the  set 
screw  from  interfering  with  the  free  rotation  of  the  nut  after  the 
screw  is  loosened.  When  the  bolt  is  placed  near  the  outside  of 
the  work  as  in  connecting  rods  the  lock  ring  is  omitted,  the  bolt 
hole  being  counter-bored  to  receive  the  projection  on  the  under 
side  of  the  nut,  and  a  threaded  hole  for  the  set  screw  being  tap- 
ped through  from  the  outside. 

The  following  empirical  equations  give  satisfactory  proportions 
where  D  is  the  nominal  diameter  of  the  bolt  and  G  the  diameter 
of  the  set  screw. 

A=  1JD--A". 

B  =  A  +  4  H. 

E  =  A  —  I". 

G  =  iD  +  i". 

H  =  JD  +  A"- 

T  =  f  D  to  D. 

T,  =  2G. 

9.  Washers. — A  washer  should  be  placed  underneath  a  nut 
or  bolt  head  when  by  reason  of  the  nature  of  the  material  or  the 
size  of  the  bolt  hole  a  suitable  bearing  surface  is  not  otherwise 
provided.  When  the  bearing  is  on  metal,  a  washer  cut  or  punched 
from  wrought  iron  or  steel  plate  is  used.  The  standard  proportions 
adopted  by  the  manufacturers  on  October  9,  1895  are  given  hi 
Table  m. 

When  the  bearing  is  on  wood  or  masonry  it  is  desirable,  unless 
the  load  be  light,  to  distribute  the  pressure  over  a  greater  area  and 
a  cast  iron  washer  of  a  form  shown  in  Fig.  9  should  be  used.  Good 
proportions  for  these  washers  are  given  in  Table  IV.  The  nomi- 


SCREW  FASTENINGS 


19 


nal  diameter  of  a  washer  is  the  same  as  the  diameter  of  the  bolt 
with  which  it  is  used.  Specify  the  nominal  diameter  of  the 
washer. 

TABLE   III. 
STANDARD  WROUGHT  IRON  AND  STEEL  Cur  WASHERS. 


H 
U 

it 

2 
2i 


n 


18 
16 
16 
14 
14 

12 
12 
10 
10 
9 


1 

U 
U 


S-- 


U 
If 

If 
1J 
2 

2i 
2f 


:-- 

~zT 

!f 


f 

3 

4f 


si 

II 


FIG.  9. 

TABLE  IV. 
CAST  IRON  WASHERS. 


Diamet 
of  Hole. 


5s 


TH 

ij; 


=  •= 


21 


10.  Screws  for  Metal. — In  general  the  purpose  of  a  screw  is  to 
draw  together  two  or  more  pieces  of  material  by  means  of  its  head 
and  the  action  of  its  thread  when  entering  the  tapped  hole  in  the 


20  SCREW  FASTENINGS 

last  of  these  pieces.  The  screw  passes  freely  through  holes  drilled 
in  each  of  the  other  pieces.  A  screw  is  not  well  suited  to  resist  a 
tendency  of  the  pieces  to  slide  over  each  other  but  is  sometimes 
used  for  that  purpose  when  the  load  is  small.  The  following 
symbols  will  be  used  in  the  description  of  screws. 

D    =  diameter  of  screw. 

L  =  length  from  under  side  of  head  to  extreme  end  of  thread, 
except  for  flatsunk  and  French  heads  and  set  screws. 

S     =  length  of  perfect  screw  thread. 

The  proportions  given  here  are  approximate  and  for  drafting  only. 

(a)  Cap  Screws. — Cap  screws  differ  from  tap  bolts  chiefly  in 
their  smaller  and  more  finished  heads,  in  the  greater  number  of 
forms  for  the  heads,  and  in  the  relative  lengths  of  their  threaded 
portions.  They  are  to  be  preferred  to  them  in  places  where  finish 
is  a  deciding  element.  They  resemble  machine  screws  in  the  forms 


of  their  cut  heads  but  the  latter  are  designed  for  much  lighter 
service.  The  range  of  sizes  of  the  two  kinds  overlap  to  some 
extent  but  owing  to  the  different  system  of  measuring  sizes  they 
are  in  no  wise  interchangeable. 

The  proportions  for  the  heads  of  cap  screws  have  never  been 
standardized  and  vary  slightly  as  produced  by  different  makers. 
The  proportions  given  in  Fig.  10  are  accurate  enough  for  general 
purposes  but  wherever  exact  values  are  needed  they  should  be 
obtained  from  the  catalogs  of  the  maker  from  whom  the  screws 


SCREW  FASTENINGS 


are  to  be  purchased.  These  heads  differ  both  in  name  and  in 
proportions  from  the  similar  forms  for  machine  screws  adopted 
by  the  American  Society  of  Mechanical  Engineers. 

Stock  forms  of  cap  screws  have  United  States  Standard  or  full  V 
thread,  with  square,  hexagonal,  round,  filister,  button,  flat,  or 
French  heads,  as  shown  in  Fig.  10 (a),  (b),  (c),  (d),  (e),  (f)  and 
(g)  respectively.  S  =  f  L  up  to  V  diameter  by  4"  long,  and  ^  L 
for  larger  sizes.  Lengths  vary  by  J"  from  f"  to  5",  except  that 
screws  with  square  or  hexagonal  heads,  Fig.  10(a)  and  (b),  are 
carried  in  a  J"  length.  Diameters  and  threads  per  inch  are  the 
same  as  for  bolts  having  the  same  form  of  thread.  Specify  the 
diameter,  form  of  thread,  length  and  head. 

(b)  Machine  Screws. — The  term  "machine  screw"  has  been 
applied  to  cover  numerous  forms  of  small  screws  having  heads  slot- 
ted so  that  they  may  be  driven  with  a  screw-driver.  The  diameter 
of  these  screws  is  designated  by  a  number  instead  of  inin  ches, 
there  being  a  uniform  difference  of  slightly  less  than  ^j"  in  the 
diameters  of  the  successive  numbers.  The  manufacturers  differed 
so  much  in  the  number  of  threads  per  inch  in  these  screws  that  the 
American  Society  of  Mechanical  Engineers  has  established  a 
standard  in  order  that  these  screws  might  be  made  interchangeable, 
and  that  standard  only  will  be  treated  in  this  book  as  it  is  neces- 
sary to  consult  the  catalogs  of  the  respective  makers  for  other 

TABLE  V. 
A.  S.  M.  E.  STANDARD  MACHINE  SCREWS. 


1 

1 

t)  o 
rt  C 

M-l           tf) 

1 

1 

9,4 

*0       ce 

1 

.2 

S£ 

|l! 

a 
s 

§ 

ll 

!"§  § 

55 

Q 

Pi 

* 

S 

H£ 

*** 

2 

0.086 

64 

A-  i 

14 

0.242 

24 

1-2 

3 

0.099 

56 

A-  f 

16 

0.268 

22 

|-2i 

4 

0.112 

48 

18 

0.294 

20 

5 

0.125 

44 

A~  1 

20 

0.320 

20 

i_2i 

6 

0.138 

40 

A~i 

22 

0.346 

18 

I-34 

7 

0.151 

36 

i-i| 

24 

0.372 

16 

N 

8 

0.164 

36 

i_ji 

26 

0.398 

16 

9 

0.177 

32 

i_i  1 

28 

0.424 

14 

1-3 

10 

0.190 

30 

H* 

30 

0.450 

14 

1  -3 

12 

0.216 

28 

l-if 

22  SCREW  FASTENINGS 

standards.  The  numbers  most  commonly  used,  with  the  threads 
per  inch  and  available  lengths  are  given  in  Table  V.  The  diameter 
of  the  screw  must  not  exceed  the  diameter  given  in  the  table  but 
may  be  a  few  thousandths  less.  The  thread  is  United  States 
Standard. 

The  stock  forms  have  flat  filister,  oval  filister,  round,  flat,  or 
French  heads,  shown  in  Fig.  ll(a),  (b),  (c),  (d)  and  (e),  all  except 
the  last  of  which  have  been  given  standard  proportions  by  the 
American  Society  of  Mechanical  Engineers  and  exact  values  are 
obtainable  from  tables  in  Vol.  28  of  the  Transactions.  The  pro- 


E 


Round. 
(c) 

FIG.  11. 

portions  given  in  Fig.  11  are  sufficiently  accurate  for  most  pur- 
poses. The  heads  differ  both  in  name  and  in  proportions  from 
those  for  cap  screws.  The  stock  lengths  vary  by  ?$"  from  A-"  to 
£",by  I"  from  \"  to  \\"  and  by  J"  from  Ij"  to  3".  The  thread 
extends  the  full  length  of  the  body  of  the  screw.  Specify  number, 
length  and  head  in  a  bill  of  material. 

(c)  Set  Screws. — Set  screws  differ  radically  from  other  screws 
in  their  action.  They  pass  through  a  threaded  hole  in  one  member 
until  the  point  of  the  screw  bears  firmly  against  the  second  mem- 
ber in  order  to  secure  a  grip  to  prevent  relative  sliding  between  the 
two  members  or  to  push  the  members  apart.  The  points  are  made 
in  various  shapes,  as  shown  in  Fig.  12 (a),  (b),  (c)  and  (d),  and 
hardened  to  resist  wear.  Of  these  forms  the  cup  point,  Fig.  12 (a), 


SCREW  FASTENINGS 


23 


is  so  generally  preferred  that  it  is  furnished  unless  otherwise  speci- 
fied. The  standard  square  head  which  is  the  form  furnished  unless 
otherwise  specified,  is  approximately  cubical, 
as  shown  in  Fig.  12,  but  low  head  and  head- 
less screws  are  also  furnished  if  desired.  The 
low  head  has  a  thickness  of  one-half  that  of  the 
standard  square  head.  Formerly  the  headless 
set  screws  were  slotted  to  be  turned  up  with 
a  screw-driver  but  in  many  cases  it  was  impos- 
sible to  get  the  screw-driver  in  position  to  use 
and  often  the  screws  were  split  apart  in  setting 
up.  In  a  more  modern  form,  sometimes  known 
as  a  safety  set  screw,  the  end  is  recessed,  as 
shown  in  Fig.  13,  to  fit  the  end  of  a  square,  hexa- 
gonal or  fluted  bar  of  steel  which  has  been  bent 
at  right  angles  to  form  a  wrench  by  means  of 
which  it  may  be  tightened.  Stock  forms  have 
United  States  Standard  or  full  V  thread  with 
diameter  and  number  of  threads  per  inch  the 
same  as  for  bolts  of  the  same  form  of  thread. 
The  thread  extends  the  full  length  of  the  body 
FIG.  12.  Q£  |-ne  screw>  The  lengths  include  point  and 

vary  by  J"  from  J"  to  I"  and  by  J"  from  I"  to  5".  Stock  diame- 
ters run  up  to  lj".  Specify  the  diameter,  form  of  thread,  length, 
point  and  head  in  the  bill  of  material. 


FIG.  13, 

11.  Screws  for  Wood. — Screws  used  in  wood  serve  the  same 
general  purpose  as  those  for  metal  but  they  have  a  distinctly 
different  form  of  thread  and  point.  The  thread  resembles  the  V 
thread  carried  down  to  about  one-half  depth,  leaving  the  root 


24  SCREW  FASTENINGS 

flat,  as  shown  in  Fig.  14.  It  is  not  necessary  to  know  the  pitch  of 
the  threads  as  the  screw  forms  the  thread  in  the  wood  in  the  process 
of  driving.  These  screws  may  have  either  gimlet  point,  Fig.  14 (a), 
for  driving  with  a  screw-driver,  or  cone  point,  Fig.  14  (b),  for 
driving  with  a  hammer.  The  former  is  standard  for  most  work  and 
is  usually  supplied  unless  otherwise  specified. 

(a)  Lag  Screws. — Lag  screw  heads  are  of  the  same  general  form 
and  proportions  as  the  heads  for  bolts  as  shown  in  Fig.  6 (a)  and 
(b)  on  page  13,  and  the  diameters  and  lengths  vary  in  the  same 
manner  up  to  V  in  diameter  and  12"  in  length.  The  length  is 
measured  from  the  point  to  the  under  side  of  the  head.  The  stock 
forms  have  square  or  hexagonal  heads  and  gimlet  or  cone  points. 
They  are  used  in  wood  when  the  conditions  are  similar  to  those 
under  which  tap  bolts  would  be  used  in  metal.  Specify  the 
diameter,  length,  head  and  point. 


Gimlet.  Cone, 

(a)  (b) 

FIG.  14. 

(b)  Hanger  Screws. — Hanger  screws  differ  from  lag  screws  in 
that  the  heads  have  been  replaced  by  nuts  the  forms  and  threads 
of  which  are  the  same  as  shown  for  bolts  in  Fig.  6  (a)  and  (c)  on 
page  13.     They  are  used  in  wood  when  the  conditions  are  similar 
to  those  under  which  a  stud  would  be  used  in  metal.     The  stock 
sizes  are  the  same  as  for  lag  screws,  but  the  length  is  measured  from 
point  to  the  outer  end  of  thread  for  the  nut.     The  stock  forms  have 
one  square  or  hexagonal  nut  and  gimlet  or  cone  point.     Specify 
diameter,  length,  nut  and  point. 

(c)  Wood  Screws. — Wood  screws  are  used  for  light  work  cor- 
responding to  that  for  which  machine  screws  are  used  in  metal. 
Their  diameters  and  lengths  are  measured  in  the  same  manner  as 
for  machine  screws.     They  are  carried  in  stock  in  round,  flat 
and  French  heads  and  gimlet  point  only.     These  forms  of  heads 
are  the  same  as  those  shown  for  machine  screws  in  Fig.  ll(c),  (d) 
and  (e)  on  page  22.     The  stock  diameters  and  lengths  are  given 
in  Table  V  on  page  21.     Specify  number,  length  and  head. 


CHAPTER  III. 


KEYS  AND  TAPER  PINS. 

12.  Use  of  Keys. — Keys  are  used  primarily  to  prevent  rotation 
of  gears,  pulleys,  etc.,  relative  to  the  shafts  upon  which  they  are 
mounted.  This  is  accomplished  by  fitting  the  key  so  that  it 
stands  parallel  to  the  axis  of  the  shaft,  partly  within  the  shaft  and 
partly  within  the  hub  of  the  gear  or  pulley  as  shown  in  end  view 
in  Fig.  15.  The  grooves  or  recesses  cut.  in  the  hub  and  shaft  to 
receive  the  key  are  called  keyways  or  key  seats.  Well  fitted  keys 
may  also  prevent  in  some  degree  the  tendency  of  the  keyed  mem- 
bers to  slide  along  the  shaft.  In  heavy  machinery  subject  to  shock 


FIG.  15. 

two  keys  placed  90°  apart  are  often  used.  When  so  placed  they 
insure  the  advantage  of  contact  at  three  places  even  chough  the 
hub  and  shaft  are  not  accurately  flitted. 

13.  Forms  and  Proportions  for  Keys. — Special  conditions  may 
justify  the  use  of  a  great  variety  of  forms  of  keys.  Only  those 
forms,  however,  which  have  become  standardized  and  are  found 
in  general  practice  will  be  discussed  in  this  book. 

All  of  these  standard  forms  are  of  uniform  width  throughout  their 
lengths.  They  should  fit  the  sides  of  the  key  seats  accurately. 
Straight  keys  are  also  of  uniform  thickness  while  taper  keys  vary 
uniformly  in  thickness  from  end  to  end.  Each  of  these  forms  may 
be  either  square  or  rectangular  in  cross  section  and  are  called 
square  keys  and  flat  keys  respectively.  The  length  of  the  key  de- 
pends on  the  length  of  hub  of  the  keyed-on  member  and  is  usually 
about  \"  longer.  When  the  point  of  a  driven  key  is  not  accessible, 
a  gib  or  head,  as  shown  in  Fig.  16,  is  formed  on  the  other  end  for 
the  purpose  of  withdrawing  the  key,  the  proportions  of  the  key 

25 


KEYS  AND  TAPER  PINS 


remaining  otherwise  unchanged.  The  gib  is  seldom  required  on  a 
straight  key.  The  measurements  of  key  and  key  seats,  illustrated 
in  Figs.  15  and  16,  are  made  as  follows: 

A  =     width  of  key  =  length  of  gib, 
B  =  thickness  of  key  =  height  of  gib, 
C   =  depth  of  key  seat  in  shaft, 
C'  =  depth  of  key  seat  in  hub, 
L  =  length  of  key. 

Straight  Keys. — Keys  without  taper  are  used  in  machine  tools 
and  where  accurate  centering  is  required.     Theoretically,  they 


FIG.  16. 

should  bear  on  the  sides  only.  Such  keys  are  usually  square  in 
cross  section.  Since  the  shafts  of  machine  tools  are  designed  for 
extra  stiffness  these  keys  are  smaller  in  proportion  to  the  size  of  the 
shaft  than  are  the  keys  on  line  shafts  which  are  usually  of  this  same 
form.  This  is  best  shown  by  a  comparison  of  the  sizes  given  in 
Tables  VI  and  VII. 

TABLE  VI. 
SQUARE  KEYS  FOR  MACHINE  TOOLS 


Diameter  of  Shaft. 


Size  of  Key. 


Diameter  of  Shaft. 


Size  of  Key. 


iXi 

*Vx& 

1x1 


21-3H 
4-5& 
5^-6^ 
7-8M 
9  -10H 
11  -12H 


ttx  ft 

HX  H 
MX  tt 


1&X1& 


The  keyed  piece  may  be  prevented  from  sliding  by  means  gf  set 
screws  through  the  hub,  bearing  on  the  top  of  the  key,  but  this 
method  tends  to  throw  the  keyed  member  off  center. 

Flat  keys  without  taper  (except  at  the  point,  which  may  be 
relieved  slightly  to  assist  in  starting  the  key)  are  fitted  to  drive, 
bearing  on  all  four  sides.  They  are  used  on  work  subject  to  shock 


KEYS  AND  TAPER  PINS 


27 


TABLE   VII. 
KEYS  FOR  SHAFTING. 


Diameter  of  Shaft. 

Size  of  Key 

Diameter  of  Shaft. 

Size  of  Key. 

t-H 

i*  I 

5^-5f 

1|X1| 

IX  I 

5H-6| 

1|X1| 

li|-2| 

IX  I 

if  xi| 

2&-21 

IX  I 

7A-8| 

2  Xl| 

fx  f 

2|X1| 

3A-31 

IX  I 

0^     1Q1 

2|xii 

1  XI 

lixif 

11^-121 

2|X1| 
3  X2 

41-51 

llXlf 

12^-131 

3iX2 

and  heavy  loads,  such  as  in  keying  cranks  and  flywheels  to  engine 
shafts  where  the  tendency  to  push  the  shaft  out  of  center  is  resisted 
by  the  close  fitting  of  the  hub.  The  thickness  is  usually  about  five- 
eighths  of  the  width.  Standard  proportions  are  given  in  Table 
VIII. 

TABLE  VIII. 
FLAT  KEYS. 


Diameter  of  Shaft. 

Size  of  Key. 

Diameter  of  Shaft. 

Size  of  Key. 

-1 

iX& 

3ft-3i 

IX  I 

*IWI 

Y^XTS 

3^^ 

1  X  I 

WMi 

fxi 

4^-5 

HXH 

S-if 

AX& 

WH 

ifx  H 

1H-2 
2&-2* 

^x^ 

IX  I 

6^-7 

7^-8 

HX  I 
ifxi 

2^-3 

gcg 

Straight  keys,  either  square  or  flat,  are  usually  purchased  in  long 
bars  which  have  been  cold  drawn  to  the  exact  section  desired  and 
from  which  keys  may  be  cut  to  any  desired  length.  Specify  width, 
thickness  and  length  in  the  order  named. 

Taper  Keys. — Taper  keys  are  used  to  prevent  sliding  as  well  as 
turning  of  the  keyed-on  member.  They  are  also  used  in  work 
subject  to  shock  and  heavy  loads,  such  as  in  keying  cranks  and 
flywheels  to  engine  shafts,  and  for  fastening  pulleys  and  gears  to 
shafts,  etc.  The  standard  taper  for  the  thickness  is  J"  per  foot  of 
length.  As  these  keys  bear  on  all  sides  one  of  the  key  seats  must 
also  be  tapered.  This  taper  is  made  in  the  key  seat  in  the  hub. 
Members  to  be  fastened  with  taper  keys  should  fit  the  shafts  very 


KEYS  AND  TAPER  PINS 


closely;  otherwise  driving  the  key  will  throw  them  off  center. 
The  thickness  of  taper  keys  is  measured  at  the  large  end.  The 
form  of  the  cross  section  at  that  end  may  be  either  square  or  flat. 
The  proportions  given  in  Tables  VII  and  VIII  apply  equally  well 
to  taper  keys. 

Tapered  square  keys,  with  or  without  gib,  are  listed  by  manu- 
facturers, with  cross  sections  from  J"  to  3"  square  varying  by  tV' 
and  with  lengths  from  If"  to  24"  varying  by  f  ".  Flat  tapered 
keys  are  not  listed  except  as  made  to  order.  Specify  width,  thick- 
ness and  length  in  the  order  named. 

For  the  purpose  of  comparison,  the  proportions  adopted  for  use 
by  a  few  of  the  larger  users  of  keys  are  given  in  Table  IX  in  which 
D  denotes  the  diamter  of  the  shaft. 

TABLE  IX. 
PROPORTIONS  OF  KEYS. 


U.  S.  Navy  Sf  d. 

Jones  &  Laughlin. 

Porter-Allen  Co. 

Width 
Thickness 

AD  +  1" 

AD  +  *' 

ID 
AD  +  &' 

iD  +  f" 

^D  +  0.16" 

Feather  Keys  or  Splines. — Where  the  keyed  piece  is  to  slide 
along  the  shaft  the  key  is  either  made  long  enough  to  provide  for 
this  motion,  or  it  is  fastened  to  the  sliding  piece  and  the  key- 
way  in  the  shaft  is  made  long  enough  to  permit  the  desired  amount 
of  sliding.  Such  keys,  called  feather  keys  or  splines,  are  frequently 
made  thicker  than  their  width  as  shown  by  the  dimensions  given 
in  Table  X.  This  additional  thickness  is  to  provide  sufficient 

TABLE  X, 
DIMENSIONS  OF  FEATHER  KEYS. 


Diameter  of  Shaft. 

Size  of  Feather. 

Diameter  of  Shaft. 

Size  of  Feather. 

-1 

IX  f 

3A-  4 

1  Xl| 

lA-li 

Ax  A 

4A-5 

1|X1| 

«Hj 

tx  * 

ST&~  6 

ifxif 

7  V      9 
T^X    T6 

6A-  7 

1|X1| 

IY§—  2 

AX  f 

7A~  8 

lfX2 

2A~2| 

ly    1 

8^     4 

8A~  9 

2  X2| 

2A~3 

fx  l 

9A-10 

2|X2| 

3A-3? 

IX  1 

KEYS  AND  TAPER  PINS  29 

surface  to  withstand  the  wear  due  to  the  sliding  contact  and  to 
resist  the  more  severe  load  conditions  due  to  the  looser  fitting  of 
the  feather  key.  Two  keys,  placed  on  opposite  sides  of  the  shaft, 
are  sometimes  used  to  improve  the  conditions  for  sliding.  They 
are  fastened  in  the  shaft  by  sunk  round  head  cap  screws,  the  diame- 
ter of  the  heads  being  about  three-fourths  the  width  of  the  feather. 
The  screws  should  enter  the  shaft  a  distance  equal  to  the  diameter 
of  the  screw.  Where  a  feather  key  is  placed  at  the  end  of  a  shaft 
it  is  sometimes  dovetailed  into  the  shaft. 

Another  form  of  feather  key  is  designed  to  fit  accurately  into  a 
key  way  of  the  form  shown  in  Fig.  19  (b)  on  page  34.  They  are  set 
into  the  shaft  a  depth  equal  to  the  width  of  the  key  and  are  fitted 
to  drive.  No  additional  fastening  is  necessary  to  secure  them  in 
place.  These  feather  keys  may  be  purchased  in  standard  sizes 
designated  by  numbers.  These  numbers  are  the  same  as  those 
given  in  Table  XI  for  Woodruff  Standard  Keys  and  the  widths  and 
lengths  agree  with  the  values  there  given  for  the  widths  and  diame- 
ters for  the  corresponding  numbers.  Specify  the  number  of  the 
key. 

14.  Woodruff  System  of  Keys.—  The  Woodruff  keys  consist  of 
circular  segments,  as  shown  in  Fig.  17,  which  are  set  in  key  ways  cut 


FIG.  17. 

in  the  shafts  by  means  of  milling  cutters  of  the  same  radius  as  the 
segment.  They  have  the  advantage  of  adjusting  themselves 
perfectly  to  any  taper  of  the  keyway  in  the  hub,  but  there  is  also 
the  disadvantage  that  the  keyed-on  member  must  always  be  forced 
on  over  the  key  after  the  key  is  hi  position.  These  keys  are  made 
in  a  large  number  of  standard  sizes  designated  by  numbers  and 
letters.  Fig.  17  shows  the  form  of  the  shorter  keys,  the  proportions 


30 


KEYS  AND  TAPER  PINS 


for  which  are  given  in  Table  XI.     The  sizes  suitable  for  use  in  the 
various  diameters  of  shafts  are  given  in  Table  XII. 

TABLE  XI. 
PROPORTIONS  FOR  WOODRUFF  STANDARD  KEYS. 


Number 
of  Key. 

"S 

SK 

cd  h 

f 

3 

_d  >» 
Ifl 
M 

Depth  of 
Keyway. 

Distance  from 
Top  to  Center 
of  Key. 

Number 
of  Key. 

1, 

1 

i 

J 

^^ 

|M 

^•s 

Depth  of 
Keyway. 

Distance  from 
Top  to  Center 
of  Key. 

A 

B 

C 

D 

A 

B 

C 

D 

1 

iV 

V 

ft 

B 

1 

A 

A 

$ 

2 

A 

^ 

& 

16 

1] 

A 

A 

A 

3 

i 

iV 

A 

17 

u 

A 

^r 

A 

4 

A 

& 

A 

18 

u 

i 

4 

i 

& 

5 

i 

ft 

X 

C 

1 

A 

A 

A 

6 

j 

\  - 

A 

A 

TV 

19 

A 

^_ 

A 

7 

i 

iV 

A 

20 

"64 

A 

8 

i 

*V 

ft 

21 

i 

I 

A 

9 

t 

A 

A 

D 

xV 

A 

A 

10 

1 

A 

£ 

ft 

E 

f 

A 

A 

11 
12 

j 

: 

A 
A 

i 

A 
ft 

22 
23 

j 

. 

, 

i 

| 

i 

A 
13 
14 

{ 

1 

f 

A 

A 

I 

ft 
ft 
ft 

F 
24 
25 

ij 

l\ 

, 

i 

1 

7 
67 

15 

1 

i 

i 

4 

G 

y 

1 

8 

rV 

A 

TABLE  XII. 


Diameter  of  Shaft. 

Number  of  Key. 

Diameter  of  Shaft. 

Number  of  Key. 

11 

1 
2,4 
3,5 
3,5,7 

If  -& 

U1    5 
*•  8 

11,  13,  16 
12,  14,  17,  20 
14,  17,  20 
15,  18,  21,  24 

U 

1A-1  i 

6,8 
6,  8,  10 
9,  11,  13 
9,  11,  13,  16 

lrl-2* 

18,  21,  24 
23,25 
25 

In  the  longer  keys  the  distance,  D,  is  considerably  increased, 
otherwise  the  form  of  the  key  differs  only  in  the  squaring  of  the 
ends  that  project  above  the  shaft.  Sometimes,  where  longer  keys 


KEYS  AND  TAPER  PINS 


31 


are  desirable,  two  or  more  keys  of  the  shorter  form  are  set  in  the 
shaft  end  to  end.     Specify  the  number  of  key  in  the  bill  of  material. 

15.  Keyways  or  Key  Seats. — Practice  is  not  wholly  uniform  as 
to  the  relative  depths  of  the  key  ways  in  the  shaft  and  in  the  hub. 
In  the  United  States  the  ordinary  practice  is  to  make  the  depth  of 
each  equal  to  one-half  the  thickness  of  the  key.     This  depth  is 
measured  at  the  side  of  the  keyways  as  shown  in  Fig.  15  on  page  25. 
For  a  taper  key  the  keyway  in  the  hub  is  tapered  and  its  depth  is 
measured  at  the  deeper  end. 

16.  Taper  Pins. — Taper  pins  are  used  to  prevent  rotational  or 
axial  sliding  between  bodies  through  which  they  pass.     The  holes 
for  tapered  pins  are  reamed  to  the  same  taper  as  the  pin  and  the  pin 
is  driven  tight.     They  may  also  be  used  in  the  place  of  keys  in 
light  work.     Standard  taper  pins  (usually  called  "Pratt  &  Whitney 
Standard  Taper  Pins")  have  a  uniform  taper  of  J"  in  diameter  per 


FIG.  18. 

foot  of  length.  The  length  is  measured  from  end  to  end  of  the 
uniform  taper  as  shown  in  Fig.  18,  the  ends  being  convex.  They 
are  made  in  standard  diameters  designated  by  numbers  and  with 


TABLE  XIII. 
PROPORTIONS  FOR  TAPER  PINS. 


Number. 

Length,  L. 

Diameter,  D. 

Number. 

Length,  L. 

Diameter,  D. 

Minimum. 

Maximum. 

I 

X 

< 

Minimum. 

a 

I 

< 

00 
0 

1 

2 
3 
4 

j 
j 

j 

. 

^  CO  CO  CO  CO  tO 

MIMMIM  ton- 

0.136 
0.156 
0.172 
0.193 
0.219 
0.250 

¥ 

X 
f 

5 
6 

7 
8 
9 
10 

1 

U 
U 

if 

4 
5 
5 
5 
6 
6 

0.289 
0.341 
0.409 
0.492 
0.591 
0.706 

ft 

32  KEYS  AND  TAPER  PINS 

lengths  varying  by  J".  The  exact  and  approximate  diameters  of 
the  large  end  and  the  stock  lengths  for  the  different  sizes  are  given 
in  Table  XIII. 

The  limits  of  the  stock  lengths  and  diameters  listed  by  differ- 
ent makers  vary  slightly.  The  range  included  in  Table  XIII 
may  be  considered  representative  of  ordinary  practice.  Specify 
number  and  length  of  pin. 


CHAPTER  IV. 

SHAFTING  AND  SHAFT  FITTINGS. 

17.  Shafting. — A  shaft  consists  of  a  long,  cylindrical  bar  of 
wrought  iron  or  steel  so  mounted  in  bearings  that  it  may  rotate 
about  its  own  longitudinal  axis,  transmitting  this  rotation  to  other 
machine  parts  which  are  attached  to  it.     That  portion  of  the  shaft 
which  lies  within  the  bearing  is  designated  as  the  journal.     The 
bearings  are  sometimes  called  journal  boxes  or  simply  boxes. 
Shafting  is  the  term  applied  to  the  stock  material  of  cylindrical 
form  from  which  shafts  are  made.     Formerly  wrought  iron  was  the 
material  chiefly  used.     It  was  rolled  when  hot  into  cylindrical  bars 
and  when  cold  turned  in  lathes  to  exact  size  and  polished.     The 
stock  sizes  of  the  hot  rolled  bars  varied  by  \"  and  they  were  reduced 
TQ"  in  finishing  thus  establishing  a  set  of  stock  sizes  for  shafting 
varying  by  \ "  but  always  YG"  less  than  each  even  \"  in  diameter. 
In  later  years  the  wrought  iron  shafting  has  been  largely  supplanted 
by  steel  which  has  been  rolled  to  exact  size  when  cold,  and  is  known 
as  "cold  rolled  shafting." 

Increased  facilities  of  manufacture  and  more  exact  methods  of 
design  have  led  to  more  stock  sizes.  These  vary  by  smaller  inter- 
vals and  start  from  the  even  inches  as  a  base.  In  all  cases,  how- 
ever, where  the  interval  in  these  stock  sizes  is  greater  than  T&"  the 
old  standard  sizes  are  maintained  in  addition.  The  lists  of  some 
of  the  representative  dealers  give  diameters  varying  by  Y&"  from 
TQ"  up  to  4"  and  by  J"  up  to  5".  Shafts  above  5"  in  diameter  are 
usually  forged  to  order.  The  commercial  lengths  vary  greatly  but 
approximate  24  feet  for  full  length  pieces,  with  30  feet  as  a  maxi- 
mum. Dealers  furnish  shafting  to  specified  lengths.  A  small  extra 
charge  is  made  for  pieces  under  12"  or  over  24  feet  in  length. 
These  limits  vary  somewhat  with  the  different  dealers. 

18.  Keyways. — Machine  parts  which  are  attached  to  a  shaft 
may  depend  wholly  upon  the  tightness  of  their  grip  and  friction 
for  the  driving  power  received  but,  except  for  light  loads,  it  is 
customary  to  make  the  connection  positive  by  inserting  keys  as 

33 


34  SHAFTING  AND  SHAFT  FITTINGS 

described  in  article  15  on  page  31.  Owing  to  the  improved  facili- 
ties possessed  by  the  makers  and  the  larger  dealers  for  cutting  the 
keyways  in  shafting,  it  is  usually  advisable  to  purchase  shafting 
with  the  keyways  cut  to  order.  These  keyways  may  be  cut  with 
an  ordinary  milling  cutter  having  a  width  equal  to  the  width  of  the 
key,  which  leaves  the  ends  curved  to  the  radius  of  the  cutter  as 
shown  in  Fig.  19(a),  or  they  may  be  cut  with  an  "end  mill"  having 
a  diameter  equal  to  the  width  of  the  key.  In  keyways  cut  with  an 
end  mill  the  ends  may  be  left  semi-circular  as  shown  in  Fig.  19(b), 
or,  after  cutting  with  the  "end  mill,"  the  ends  of  the  key  way  may 
be  cut  out  square  as  shown  in  Fig.  19  (c),  by  chipping  with  a  cape 


«)  (b)  (c) 

FIG.  19. 

chisel.  These  forms  are  increasingly  expensive  in  the  order  given 
on  account  of  the  additional  labor  and  equipment  required.  Key- 
ways  of  the  second  form  of  limited  size  may  be  cheaply  made  in 
small  shafts  for  machine  tools. 

19.  Couplings. — As  stated  in  article  17,  shafting  is  made  in 
relatively  short  pieces  which  must  be  fastened  together  end  to  end 
when  in  place  so  that  their  centers  shall  at  all  times  be  truly  aligned. 
Many  of  these  fastenings  may  be  of  a  permanent  nature  while 
others  must  be  of  a  nature  to  permit  disconnection  at  frequent 
intervals.     Those  of  the  latter  class  are  commonly  called  clutches 
or  clutch  couplings. 

20.  Permanent  Couplings. — There  are  several   types  of  per- 
manent couplings.     For  very  light  work  a  sleeve  coupling  may  be 
used.     This  consists  of  a  simple  sleeve,  as  shown  in  Fig.  20,  into 


SHAFTING  AND  SHAFT  FITTINGS  35 

which  the  ends  of  the  shafts  may  be  inserted  and  secured  by  set 
screws.  It  is  necessary  that  the  heads  of  these  set  screws  shall  be 
sunk  into  the  sleeve  or  that  headless  set  screws  be  used  to  avoid 


20. 


danger  to  workmen.  Sometimes,  where  keyways  in  the  shaft  are 
objectionable  or  have  not  been  provided,  keyless  couplings  are 
used  in  which  the  grip  on  the  shaft  is  frictional  only.  The  neces- 
sary pressure  is  obtained  by  forcing  the  halves  of  a  sleeve  together 
by  means  of  rings  driven  over  the  tapered  ends  of  the  sleeve  as 
shown  in  Fig.  21.  or  by  forcing  a  sleeve  on  over  a  tapered  bushing 
by  means  of  bolts  as  illustrated  in  Fig.  22. 


Where  a  more  positive  connection  is  desired  keys  may  be  used 
with  a  sleeve  in  which  case  it  is  made  in  halves,  as  shown  in  Fig.^23, 
to  bolt  together  over  the  keys  when  they  are  in  place.  It  would 


36 


SHAFTING  AND  SHAFT  FITTINGS 


otherwise  be  necessary  to  make  the  keyways  in  the  shafts  extend 
beyond  the  sleeve  an  amount  equal  to  the  length  of  the  key,  to 


allow  the  key  to  be  inserted.     Any  of  these  couplings  which  tight- 
en up  on  the  shafts  are  known  as  compression  couplings. 


FIG  24. 

A  positive  connection  may  also  be  obtained  by  the  use  of  flanged 
couplings,  illustrated  in  Fig.  24  and  shown  in  section  in  Fig.  25. 
These  couplings  are  generally  finished  all  over  and  the  overhanging 


FIG.  25. 


SHAFTING  AND  SHAFT  FITTINGS 


37 


rim  prevents  danger  from  the  clothing  of  workmen  catching  on  the 
bolt  heads  or  nuts.  The  bolt  holes  are  reamed  for  coupling  bolts 
as  described  in  article  7  on  page  14.  These  bolts  are  made  to  fit 
the  holes  accurately  in  order  that  each  bolt  shall  take  its  share  of 
the  load.  The  accurate  centering  of  the  shafts  is  secured  by 
extending  one  of  them  entirely  through  its  coupling  until  it  enters 
the  mating  coupling  on  the  other  shaft  or,  at  an  added  expense,  the 
face  of  one  of  the  flanges  may  be  recessed  to  receive  a  corresponding 
projection  on  the  face  of  the  other  as  shown  in  section  in  Fig.  26. 
The  following  empirical  equations  were  derived  from  the  com- 
mercial cast  iron  couplings  of  one  of  the  leading  makers.  The 


FIG.  26. 


dimensions  determined  from  these  equations  are  to  be  taken  to  the 
next  larger  or  the  nearest  3^"  or  f  "  according  to  the  judgment  of  the 
draftsman. 


A 
B 

C 
D 
E 
F 


J 
K 


diameter  of  shaft. 
If  A  +  i". 
If  A  +  2  d  +  If". 
If  A  +  4  d  +  If. 


I  +  d.  but  not  <  (2  I  —  G.) 
iA  +  Jf"  (sizes  1J"  —  3|"), 
f  A  +  f  (sizes  SI"--  12"). 
+  }". 

+     A"     but     not     less 
+  iV'  but  not  less  than  |". 

+  i". 


than     |". 


38  SHAFTING  AND  SHAFT  FITTINGS 

n  =  number  of  bolts  =  f  A  +  3. 

d  =  diameter  of  bolts  =   f  A  +  &"• 

I  =  length  of  bolts  =  G  +  d  +  I". 

21.  Clutch  Couplings. — There  are  two  general  classes  of  clutch 
couplings;  jaw  clutches,  in  which  there  is  a  positive  connection 
made  by  the  interlocking  of  projecting  parts,  called  jaws;  and 
friction  clutches,  in  which  the  connection  is  wholly  fractional  and 
produced  by  forcing  blocks  of  wood  or  other  material  firmly 
against  a  disk  of  metal. 

Jaw  Clutches  are  made  either  with  square  jaws,  Fig.  27 (a),  or 
with  spiral  jaws,  Fig.  27(b).  One  set  of  jaws  is  keyed  firmly  to  the 
end  of  one  of  the  shafts  while  the  mating  set  slides  on  a  feather  key 
in  the  other  shaft  to  mesh  or  release  as  desired.  The  number  of 


/         (a) 

;  .    . 

jaws  is  usually  two  or  three,  varying  with  the  size  of  the  clutch. 
The  angles  between  the  successive  jaws  must  be  accurately  con- 
structed in  order  that  the  load  may  be  properly  divided  between 
the  jaws.  Those  with  spiral  jaws  are  more  easily  thrown  in  but 
will  drive  in  one  direction  only,  and  hence  must  be  made  in  right- 
hand  and  left-hand  shapes.  Square  jawed  clutches  will  operate 
in  either  direction  but  require  a  small  amount  of  backlash  (rota- 
tional play  between  the  jaws  when  in  mesh)  to  facilitate  throwing 
in.  It  is  necessary  that  the  end  of  the  driven  shaft  shall  be  con- 
tinously  sustained  in  alignment  with  the  driving  shaft.  For  this 
purpose  there  is  inserted  into  the  jaw  which  is  fixed  to  its  shaft  a 
finished  ring  into  which  the  end  of  the  other  shaft  projects,  as  shown 
in  Fig.  27 (a).  This  ring  is  made  separately  and  afterward  fastened 
in  place,  in  order  to  facilitate  the  machining  of  the  jaws.  Since 
the  ring  turns  on  the  end  of  the  shaft  when  the  clutch  is  thrown  out, 


SHAFTING  AND  SHAFT  FITTINGS 


39 


oil  holes  must  be  provided  for  lubrication.  It  is  usual  to  provide 
an  oil  hole  in  each  space  between  the  jaws  so  that  one  may  always 
be  available  when  oiling  without  turning  over  a  heavy  shaft. 
The  sectional  drawing,  Fig.  28,  shows  a  clutch  with  three  square 
jaws  and  with  the  finished  ring  removed.  The  proportions  given 
in  the  following  empirical  equations  were  derived  from  the  dimen- 


FIG.  28. 

sions  of  commercial  cast  iron  clutches  sold  by  one  of  the  leading 
makers  and  are  suitable  for  either  square  or  spiral  jawed  clutches. 
A  backlash  of  2°  is  allowed  in  the  square  jawed  clutches. 

A  =  diameter  of  shaft. 
B  =  IfA  +  f ". 
C  =  2f  A  +  1J". 
D  =  1JA  +  i". 

E  =  IA  +  i". 


40 


SHAFTING  AND  SHAFT  FITTINGS 


F  =  A  +  I". 
G  =  If  A  +  1J". 
H  =  If  A  +  J". 

J  =  iVA  +  |". 
K  =  J,A  +  yr. 

M  =  JA  +  r. 

The  finished  ring  is  also  of  cast  iron  and  is  held  in  position  by  means 
of  headless  set  screws  placed  one  at  each  jaw,  with  half  its  diameter 
in  the  ring  and  half  in  the  jaw.  The  points  of  these  screws  should 


FIG.  29. 

i 

bear  in  order  that  the  screw  may  be  tightened.  The  following 
table  gives  the  sizes  of  set  screws  used  in  the  different  sizes  of 
clutches. 


Shaft. 


Set  Screw. 


Diameter. 

Diameter. 

Length. 

H-lH 

2&-3H 

4A-6H 

i 

1 

i 

* 
1 
t 

The  sliding  jaw  is  given  an  overtravel  of  J"  for  shafts  up  to  1  fa" 
diameter,  f  "  from  Ij"  to  4Jf  ",  and  \"  above  5". 

Jaw  clutches  are  thrown  in  or  out  by  means  of  a  lever  or  shifter 
of  the  general  form  illustrated  in  Fig.  29.  This  is  connected  to  a 
collar,  Fig.  27(b),  that  runs  in  a  groove  in  the  hub  of  the  part  of  the 
clutch  which  slides  on  the  feather  key.  This  collar  is  of  cast  iron 
made  in  two  pieces  to  bolt  together  in  the  groove  as  is  shown  in  the 
key  drawing,  Fig.  30,  to  which  the  following  empirical  proportions 
apply. 


SHAFTING  AND  SHAFT  FITTINGS 


41 


FIG.  30. 


A  =  diameter  of  shaft. 
H  =  (see  Fig.  28). 
J  =  (see  Fig.  28). 
M  =  IfA  +  21". 
N  =  B  +  A"  to  B  + 
O  =  2A  +  1J". 
P  =  |A  + 

Q  =  11  P. 

R  = 
S  = 
T  = 

d  = 


iff 

8     • 


f". 


2  d  +  i". 

1JA  but  not  less  than  1}". 

dj_    i  " 
-r  -32   • 

diameter  of  bolts  =  A  A  +  A". 


1=  length  of  bolts  =  S  +  d  +  J". 

The  hub  turns  continually  in  the  collar  when  the  feather  key  is 
in  the  driving  shaft,  or  in  any  case,  when  the  clutch  is  in.  An  oil 
hole  must,  therefore,  be  provided  in  one-half  of  the  collar  in  such  a 
position  that  it  may  be  up  at  whatever  angle  the  lever  may  be 
given  in  setting  up. 

The  lever  may  be  vertical,  horizontal,  or  at  any  intermediate 
angle  as  desired  but,  in  the  middle  of  its  throw,  it  should  stand 
approximately  at  right  angles  to  the  shaft.  It  is  made  of  wrought 
iron  and  tapers  to  a  handle  at  the  end,  as  in  Fig.  29.  The  fork  i  s 
forged  in  parts  so  that  they  may  be  placed  over  the  projections  on 


SHAFTING  AND  SHAFT  FITTINGS 


the  collar  and  then  be  bolted  to  the  lever  as  shown  in  the  key  draw- 
ing, Fig.  31,  to  which  the  following  proportions  apply. 

A  =  diameter  of  shaft. 

P  =  (see  Fig.  30). 

a  =  2^A  +  If". 

b  =  1JA  +  If". 

c  =  2  P. 

e  =  P  +  *". 

f  =  If  P. 

g  =  AA  +  }". 

h  =  fg. 

k  =  Jc  +  I". 

m  =  diameter  of  bolts   =  g. 

n  =  3g. 


4 


*SM     -M"^/ 


FIG.  31. 

Friction  Clutches  are  made  in  too  many  forms  and  of  construc- 
tion too  complex  for  discussion  here  but  their  general  characteris- 
tics are  illustrated  in  Fig.  32.  A  collar  sliding  on  the  shaft  controls 
the  levers  which  operate  the  friction  grip.  Sliding  of  this  collar 
may  be  effected  by  a  hand  lever  like  that  illustrated  in  Fig.  29,  if 
the  clutch  is  small.  For  large  clutches,  a  hand  wheel  and  gears  as 
illustrated  in  Fig.  33  are  used  to  operate  the  lever.  These  clutches 


SHAFTING  AND  SHAFT  FITTINGS 


43 


are  largely  used  where  the  connection  has  to  be  made  when  the 
driving  shaft  is  in  motion  at  a  considerable  speed  since  they  avoid 


the  sudden  shock  of  a  positive  connection,  but  they  have  the  disad- 
vantage of  requiring  good  adjustment  to  prevent  slipping  under 
load. 

22 .  Collars. — A  shaft  is  prevented  from  endwise  motion  through 
the  supporting  bearings  by  means  of  collars,  Fig.  34,  which  are 
clamped  to  the  shaft  by  means  of  set  screws.  The  finished  sides 


FIG.  33. 

of  these  collars  bear  against  the  finished  ends  of  the  bearings. 
Formerly  plain  collars  of  rectangular  section  with  standard  set 
screws  were  used.  These  were  dangerous  because  of  the  projecting 
set  screw  heads  which  caught  the  clothes  of  workmen,  wind  ng 


44 


SHAFTING  AND  SHAFT  FITTINGS 


them  about  the  shaft.  Many  states  now  have  laws  prohibiting 
their  use.  The  common  headless  set  screws  which  are  slotted  so 
as  to  be  tightened  with  a  screw-driver  were  too  weak  to  be  satis- 
factory when  used  with  the  plain  collars  but  the  introduction  of 


safety  set  screws,  Fig.  13,  page  23,  has  removed  this  difficulty. 
Such  screws  used  with  the  plain  collar  should  be  short  enough  to  be 
entirely  beneath  the  surface  of  the  collar  when  tightened. 

In  the  safety  collars,  Fig.  34,  the  set  screw  head  is  surrounded 
by  a  ring  and  the  projecting  flanges  at  the  sides  protect  the  work- 
men from  contact  with  this  ring  as  it  revolves.  Safety  collars  of 


FIG.  35. 

the  general  form  shown  are  made  in  halves  that  may  be  bolted 
together  around  the  shaft  and  thus  avoid  taking  down  a  shaft  to 
put  on  an  additional  collar.  The  following  empirical  proportions 
for  safety  collars  were  derived  from  dimensions  taken  from  com- 
mercial collars  of  the  form  drawn  in  section  in  Fig.  35  and  sold  by 
one  of  the  leading  makers.  One  low  head  set  screw  is  used  for 
shafts  under  3"  in  diameter  and  two  for  larger  sizes. 


SHAFTING  AND  SHAFT  FITTINGS 


45 


d  =  diameter  of  set  screw. 
L  =  length  of  set  screw. 
A  =  diameter  of  shaft. 
B  =  A  +  2L  + 
C  =  ^A  +  f". 

D  =  *VA  +  i". 

E  =  ArA  +  I",  but  not  to  exceed  D  -f 
T  =  iL. 


One  Set  Screw 

Two  Set  Screws 

d 
L 

M 

N 

&A  +  A". 

d+r. 

2  d  +  f  ". 

2d+i 

r^A  +  |;/,  but  not  to  exceed  &  A. 

2  d  -  r. 
s^  d  +  r. 

2  d,  but  not  to  exceed  d  +  f  *. 

CHAPTER  V. 


SHAFT  FIXTURES. 

23.  General  Nature. — Under  the  head  of  shaft  fixtures  are 
included  all  of  those  fixed  parts  by  means  of  which  a  shaft  is  sus- 
tained in  its  proper  position  with  regard  to  the  building  in  which  it 
is  located.     These  fixtures  may  be  conveniently  divided  into  the 
bearings,  which  are  actually  in  contact  with  the  shaft,  and  the 
bearing  supports  intermediate  between  the  bearing  and  the  posts, 
walls,  or  floor  timbers,  which  furnish  the  ultimate  support  for  the 
shaft. 

24.  Purpose  and  Qualities  of  Bearings. — The  purpose  of  a  bear- 
ing is  to  support  a  shaft  and  to  constrain  it  to  revolve  about  its 
own  axis  while  the  bearing  remains  attached  to  some  stationary 
body.     For  this  reason  it  must  present  a  polished,  well  lubricated 
inner  surface  for  contact  with  the  surface  of  the  shaft.     This  sur- 
face must  be  of  such  material  as  to  cause  the  least  possible  damage 
to  the  shaft  in  case  of  failure  of  the  lubrication  and,  at  the  same 
time,  to  resist  wear  when  properly  lubricated.     Cast  iron  furnishes 
a  fairly  good  surface  as  long  as  it  is  well  lubricated  but,  in  case  the 
lubricant  fails,  it  does  great  damage  to  the  shaft  because  of  its 
superior  hardness.     To  save  the  shaft  the  bearing  metal  should  be 
the  softer.     Materials,  such  as  brass,  bronze,  or  babbitt  metal, 
which  combine  this  softness  with  the  requisite  wearing  qualities  are 
too  expensive  to  use  for  the  construction  of  the  whole  of  the  bear- 
ing and  are  used  simply  as  a  lining  for  the  inner  surface,  the  frame 
or  remainder  of  the  bearing  being  of  cast  iron.     In  case  of  damage 
these  linings  are  easily  replaced. 

When  the  lining  is  of  brass  or  bronze  it  is  usually  machined  to 
fit  a  correspondingly  machined  surface  of  the  cast  iron  frame. 
Linings  of  babbitt  metal,  owing  to  its  low  melting  point,  are  cast 
in  the  frame  which  is  already  completed  in  other  ways.  There 
are  grooves  or  holes,  called  anchorages,  in  the  inner  surface  of  the 
frame,  into  which  the  metal  sets  and  is  prevented  from  rotating 
or  sliding  axially.  In  the  cheaper  bearings  a  short  piece  of  shafting 

46 


SHAFT  FIXTURES  47 

of  the  proper  diameter  is  carefully  centered  in  the  frame  with  close 
fitting  collars  at  the  ends  and  the  babbitt  metal  poured  around  the 
shafting.  The  shrinkage  of  the  metal  as  it  cools  tends  to  draw 
such  linings  away  from  the  frame.  The  better  bearings  are 
poured  with  a  surplus  of  metal  which  is  afterward  hammered  into 
the  anchorages  and  the  surface  machined  to  size. 

25.  Forms  of  Bearings. — The  varying  positions  of  the  shaft, 
methods  of  supporting  the  bearings,  and  methods  of  supplying  the 


FIG.  30. 


48  SHAFT  FIXTURES 

lubricant  to  the  bearing  surfaces  have  resulted  in  so  many  forms  o! 
bearings  that  but  the  briefest  mention  may  be  made  of  them  in  this 
book.  Usually  the  shaft  is  horizontal  and  the  bearing  is  of  some 
such  form  as  shown  in  part  section  in  Fig.  36 (a).  If  it  be  vertical 
the  general  form  changes  to  that  of  Fig.  36  (b).  Since  the  set 
screws  of  the  collars  described  in  article  22  cannot  be  depended 
upon  to  support  the  weight  of  the  shaft,  there  must  also  be  pro- 
vided for  a  vertical  shaft  a  special  form  of  bearing,  known  as  a 
step  bearing,  Fig.  36 (c),  in  which  the  lower  end  of  the  shaft  rests. 
Bearings  may  be  solid,  as  in  Fig.  36 (b),  requiring  to  be  slipped  on 
over  the  end  of  the  shaft.  In  most  cases,  however,  they  are  split 
along  the  center  line  of  the  shaft,  Fig.  36(a),  so  that  it  may  easily 
be  removed.  This  also  provides  opportunity  to  take  up  looseness 
due  to  wear.  These  parts  are  designated  as  the  cap  and  the  base 
and  they  are  held  together  by  two  or  more  bolts,  known  as  the  cap 
bolts. 

A  bearing  may  be  supported  from  beneath,  requiring  a  flat 
bottom  for  the  base,  Fig.  36(a);  from  the  side,  requiring  a  vertical 
side  on  the  base,  Fig.  36(d);  or  it  may  be  suspended  on  pivots 
at  the  center,  Fig.  36 (e).  The  lubricant  may  be  supplied  through 
an  oil  hole,  Fig.  36 (d);  it  may  be  carried  from  an  oil  reservoir  by  a 
wick,  which  is  pressed  against  the  shaft,  Fig.  36(a);  or  it  may  be 
carried  up  to  the  top  of  the  shaft  from  a  reservoir  beneath  by  means 
of  rings  or  chains,  Fig.  36 (e),  which  rest  upon  and  revolve  with  the 
shaft,  while  dipping  into  the  oil  in  the  reservoir. 

26.  Adjustments  of  Bearings. — In  order  that  a  shaft  may  run 
properly  its  axis  must  be  as  near  to  straight  line  as  it  is  practicable 
to  obtain.  To  accomplish  this  straightening  or  alignment  of  the 
shaft  provision  must  be  made  so  that  the  supporting  bearings  may 
be  adjusted  either  vertically  or  horizontally  or  in  both  directions 
in  a  plane  perpendicular  to  the  axis  of  the  shaft.  One  of  these 
adjustments,  the  horizontal,  in  the  case  of  Fig.  36  (a)  and  the 
vertical  in  Fig.  36 (b)  and  Fig.  36 (d),  is  usually  provided  for  by 
elongation  of  the  holes  in  the  base  through  which  it  is  bolted  to  a 
support.  These  bolts  may  be  designated  as  the  holding  bolts  to 
distinguish  them  from  the  cap  bolts.  The  remaining  adjustment, 
or,  in  the  case  of  Fig.  36 (e),  both  adjustments,  should  be  provided 
in  the  support  for  the  bearing.  The  making  of  these  adjustments 
is  called  aligning  the  shaft. 


SHAFT  FIXTURES 


49 


In  split  bearings  provision  is  made  to  prevent  the  shaft  from 
becoming  loose  as  the  lining  of  the  bearing  wears  away.  When 
the  lining  is  new  thin  strips  of  metal  or  hard  pressed  paper,  called 
liners  or  shims,  are  placed  on  each  side  of  the  shaft  between  the 
cap  and  base  so  that  the  cap  bolts  may  be  tightened  firmly  without 
pinching  the  shaft.  These  liners  are  then  removed  one  at  a  time 


FIG.  37. 

as  the  wear  progresses  until  all  have  been  removed,  when  a  new 
lining  is  put  in  and  the  process  repeated.  In  split  bearings  the 
edges  of  the  linings  along  the  division  should  be  chamfered  so 
that  the  lubricant  may  not  be  scraped  off  and  forced  out  at  the 
joint  but  may  be  drawn  around  with  the  shaft.  This  chamfering 
should  not  extend  to  the  ends  of  the  bearing  lest  it  furnish  a  means 
of  escape  for  the  lubricant. 

Endwise  adjustment  of  horizontal  shafts  is  provided  by  means 
of  setting  the  collars  (see  article  22  on  page  43)  which  bear  against 


50  SHAFT  FIXTURES 

the  finished  ends  of  the  bearings.     In  vertical  shafts  this  adjust- 
ment is  made  by  raising  or  lowering  the  step  bearing. 

27.  Proportions  for  Babbitted  Bearings. — The  following  empiri- 
cal equations  were  derived  from  measurements  taken  from  a  simple 
form  of  commercial  babbitted  shaft  bearing,  designed  to  be  sup- 
ported from  beneath  and  having  oil  hole  lubrication  as  shown  in 
the  key  drawing,  Fig.  37.  In  small  bearings,  for  shafts  less  than 
2f "  in  diameter,  two  cap  bolts  are  used  and  holes  drilled  for  babbitt 
anchorages.  In  larger  sizes  four  cap  bolts  are  used  and  dovetail 
grooves  cored  for  the  anchorages.  To  prevent  endwise  displace- 
ment of  the  babbitt  these  anchorages  should  not  extend  to  the 
ends  of  the  bearing.  The  cap  bolts  and  holding  bolts  are  provided 
with  hexagon  nuts. 
T  A  =  diameter  of  shaft. 

d  =  diameter  of  holding  bolts  =  f  A  +  ^"but  not  to  exceed  fA. 

di  =  diameter  of  cap  bolts  =  fd. 

t  =  ^A  +  A",  but  not  to  exceed  ^ A  +  &" ,  or  \" . 

B  =  length  of  bore  =  3  A. 

C   =    1&  A  +  2  t  +  i". 

D  =  C  —  JA. 

E  =  If  A  +  4"  (4  cap  bolts), 

=  G  +  J  +  3  d  +  }A  +  \"  (2  cap  bolts). 
F  =  E  +  3  d  +  \". 
G  -  1|A  +  2-t  +  dt  +  i". 
H  =  f  A  +  1J",  but  not  to  exceed  A. 
J  =  2  i  +  f  • 
K  =  H  +  J  +  AA  +  i"  (4  cap  bolts), 

=  1JA  +  \"  (2  cap  bolts). 
L  =  |A,  but  not  less  than  JC  +  |". 
M  =  JC  —  ^A  +  J",  but  not  to  exceed  A. 
N  =  AA  +  A"  (approx.). 
P  =  JA,  but  not  less  than  £A  +  \" . 
R  =  P  - 
S  =  |A  -  I 


SHAFT  FIXTURES 


51 


T  =  2  d  +  J". 
U  =  2  d  +  I". 
V  =  JA  +  }". 

w  =  ijdi  +  i"/ 

X  =  not  less  than  di  + 

Y  =  |A  +  J". 
Z 


In  order  that  the  oil  hole  in  the  top  of  the  cap  may  be  made 
without  machining  or  coring  it  is  made  large  enough  to  mold  in 


FIG.  38. 

green  sand.  The  oil  is  prevented  from  flowing  out  around  the 
shaft  too  freely  by  filling  the  oil  well  with  cotton  waste  or  other 
absorbent  material. 

The  general  proportions  given  below,  which  apply  to  the  key 
drawing,  Fig.  38,  are  for  the  type  of  babbitted  bearing  suitable  for 
machine  frames.  The  grease  cup  shown  may  be  replaced  by  any 
suitable  form  of  oiling  device  without  other  changes  in  the  bearing. 
Through  bolts  should  be  used  whenever  possible.  If  the  bearing 


52  SHAFT  FIXTURES 

is  so  placed  that  this  is  riot  possible,  studs  or  tap-bolts  may  be 
substituted.  The  offset  in  the  division  between  the  cap  and  the 
base  is  machined  to  an  accurate  fit  and  prevents  sidewise  displace- 
ment of  the  cap.  The  cover  to  the  oil  well  being  a  separate  casting 
may  be  relatively  thin. 

A  =  diameter  of  bore. 

B  =  length  of  bore  =  A  to  4  A  to  suit  conditions. 

t  =  thickness  of  babbitt  =  rgA  +  J",  but  not  to  exceed  ^A  +  i". 

C  =  A  +  2t 

D  =  IfA  +  I". 

d  =  diameter  of  bolts   =   ^A  +  \"  . 

(use  4  except  for  short  bearings,  then  use  2)  . 


E 

=  D  +  If, 

i. 

F 

=  IB. 

G 

=  d  +  i". 

H 

=  2  d  +  i". 

J 

=    UA  + 

i/r. 

K 

=  »A  +  I" 

. 

L 

=  it. 

M 

=  A  A  +  1 

/r. 

N 

=  M  +  K. 

P 

=  JA  or  to 

suit. 

Q 

=  JA  or  to 

suit. 

R 

-tt 

S 

=  3  t  —  I" 

. 

T 

=  2  t  —  I" 

U 

=  iir  A  +  i 

V- 

V 

=  IB. 

W 

=  fU. 

X 

=  ^A  +  j3 

*"• 

28.     Quarter-box  Bearings.  —  These  bearings  get  their  name 
from  the  fact  that  the  bearing  surface  or  box  is  divided  into  four 


SHAFT  FIXTURES 


53 


parts  or  "quarters,"  Fig.  39,  each  of  which  may  be  moved  up 
against  the  journal  by  means  of  independent  adjusting  wedges  or 
screws.  By  this  means  any  wear  that  may  have  occurred  can  be 
taken  up  in  a  more  nearly  correct  manner  than  could  be  done  with 


FIG.  39. 

bearings  divided  into  but  two  adjustable  parts.  When  the  wear 
in  a  bearing  is  due  to  a  resultant  pressure  in  a  single  direction,  such 
as  the  weight  of  the  supported  shaft  alone,  a  two-part  bearing  will 
provide  the  only  needed  adjustment.  When,  however,  the  direc- 
tion of  this  resultant  pressure  changes  during  the  rotation  of  the 
shaft  it  becomes  necessary  to  provide  a  more  complete  adjustment 
to  take  up  the  wear,  and  also  to  keep  the  shaft  in  true  alignment. 


54  SHAFT  FIXTURES 

Bearings  of  this  type  are  much  used  for  steam  engines  and  are 
usually  of  quite  large  dimensions.  They  are  not  purchasable  alone. 
Either  the  base  is  a  part  of  the  engine  frame  or  it  is  a  pedestal 
designed  especially  to  be  attached  to  the  engine  frame  or  to  its 
foundation.  The  base  is  recessed  to  receive  the  parts  of  the  box 
and  the  adjusting  wedges.  A  strip  in  the  center  of  the  bottom  of 
this  recess  is  machined  to  receive  the  bottom  section  of  the  box, 
which  may  or  may  not  be  provided  with  a  vertical  adjustment  by 
liners  or  a  wedge.  A  portion  of  each  side  of  the  recess  is  machined 
to  support  the  adjusting  wedges  which  move  the  box  and  shaft 
horizontally.  This  adjustment  is  necessary  to  keep  the  correc: 
distance  between  the  center  line  of  the  shaft  and  the  center  of  the 
cylinder.  Each  of  these  wedges  is  drawn  up  by  means  of  two  studs 
passing  through  the  cap  which,  since  they  cannot  be  drawn  tight 
without  binding  the  shaft,  are  kept  in  position  by  means  of  jam 
nuts.  The  motion  of  these  wedges  should  be  sufficient  to  take  up 
wear  equal  to  one-half  the  thickness  of  the  babbitt  on  each  of  the 
side  sections  of  the  box.  The  cap  and  base  are  machined  to  an 
accurate  fit  at  the  sides  and  a  strip  in  the  center  of  the  under  side 
of  the  cap  is  machined  to  bear  on  the  top  section  of  the  box.  The 
cap  is  drawn  down  by  means  of  studs  set  in  the  top  of  the  base 
until  the  top  section  of  the  box  bears  firmly  on  liners  placed  between 
it  and  the  side  sections.  Each  of  the  sections  of  the  box  is  machined 
for  contact  with  the  adjacent  sections. 

These  boxes  when  worn  or  in  case  of  accidental  over-heating  have 
to  be  removed  to  be  relined  with  babbitt.  It  is,  therefore,  desirable 
that  it  should  be  possible,  by  loosening  the  cap  and  blocking  up 
the  shaft,  to  S*lide  them  out  and  replace  them  without  removing 
the  shaft  from  position.  Where  this  sliding  is  endwise  it  is  nec- 
essary to  attach  a  circular  plate  to  the  frame  or  pedestal  and 
around  the  shaft  or  to  provide  some  other  means  to  keep  them 
from  working  out  from  the  vibration  of  the  engine  while  run- 
ning. 

Under  normal  conditions  the  lubricant  is  oil  fed  either  from  large 
oil  cups  or  piped  to  the  bearing  from  a  tank.  In  addition  there  is 
usually  a  provision  for  an  emergency  lubrication  by  packing  a 
recess  in  the  cap  with  some  solid  grease  that  will  melt  and  flow  into 
the  bearing  should  the  temperature  rise  above  the  normal. 


SHAFT  FIXTURES  55 

There  are  many  designs  of  quarter-box  bearings,  that  of  which 
the  description  has  been  given  and  to  which  the  following  empirical 
proportions  apply,  being  one  of  the  simplest.  Some  of  the  varia- 
tions from  this  design  are,  use  of  a  single  adjusting  wedge;  sub- 
stitution of  set  screws  for  the  adjusting  wedges;  adjustment  of 
the  lower  box  by  means  of  a  wedge;  adjustment  of  the  upper  box 
by  means  of  set  screws;  and  making  the  bearing  self -oiling  by  pro- 
viding an  oil  reservoir  and  oiling  chains  running  in  suitable  chan- 
nels in  the  boxes. 

A    =  diameter  of  bore. 

B    =  length  of  bore  =  1JA  to  2JA. 

C  =  0.225A  +  1". 

D    =  |A. 

E    =  diameter  of  wedge  bolts  =  yVA  +  J". 

(Core  holes  in  cap  \"  to  \"  larger.) 
F    =  minimum  thickness  of  wedge  =  2  E. 

(Taper   =    1J"  in   12".) 
G    =  diameter  of  cap  bolts  =  A  A  +  \" . 

(Core  holes  in  cap  J"  to  \"  larger. 
H    =  2  G  +  i". 
I     =  AA  +  1". 
J     =  ArA  •  +  i". 
K    =0.45A  +  i". 

L  =  U  +  i". 

M  =  &A  +  }". 

N  =  fM. 

O  =  fM. 

P  =  IM. 

Q  =  f  M. 

R  =  f  M. 

S  =  JB. 

T  =  JA  +  I". 

u  =  IT. 

V    =i*A  +  i". 


56  SHAFT  FIXTURES 

29.  Bearing  Supports. — Bearings  may  be  attached  directly  to 
the  top  or  to  the  under  side  of  floor  timbers,  to  posts,  or  to  walls. 
It  rarely  occurs,  however,  that  the  shaft  is  brought  into  the  desired 
position  when  so  fastened.  Interposing  an  intermediate  member 


FIG.  40. 

not  only  removes  the  shaft  farther  from  the  wall,  floor,  or  ceiling 
but  may  also  provide  a  convenient  adjustment  for  aligning  the 
shaft.  These  intermediate  members  vary  in  size  and  proportion 
according  to  the  diameter  of  the  shaft  with  which  they  are  used 
and  with  the  distance  of  the  shaft  from  the  floor,  wall,  or  ceiling 
from  which  it  is  supported. 


FIG.  41. 

30.  Stands  and  Base  Plates. — When  the  shaft  is  to  be  supported 
from  beneath,  the  intermediate  member  may  have  the  general 
form  of  the  floor  stand,  Fig.  40.  The  stock  sizes  vary  by  6" 
in  nominal  height  up  to  42".  This  height  may,  in  each  size, 
be  varied  a  small  amount  (usually  less  than  an  inch)  by  means  of 
the  adjusting  wedges.  These  are  operated  by  means  of  the  set 
screws  and  secured  by  the  jam  nuts  shown  at  the  sides.  When  it  is 
desirable  that  the  elevation  of  the  shaft  from  the  floor  shall  be 
small  a  base  plate,  Fig.  41,  may  be  used  in  the  place  of  the  stand. 
This  may  or  may  not  have  the  provision  for  vertical  adjustment. 


SHAFT  FIXTURES 


57 


31.    Wall  Brackets. — When  the  bearing  is  to  be  supported  from 
a  wall  or  post  it  may  be  placed  upon  a  wall  bracket  as  illustrated 


Fro,  42. 


in  Fig.  42.     These  brackets  are  fastened  to  a  wall  by  means  of 
through  bolts,  or  to  wooden  posts  by  means  of  hanger  screws,  or 


l-t* 


O 

T~ 


FIG.  43. 


58 


SHAFT  FIXTURES 


lag  screws.  The  holes  in  the  bracket  for  these  fastenings  are 
elongated  vertically  to  provide  an  adjustment  for  aligning  the  shaft, 
in  order  to  reduce  the  number  of  stock  sizes  of  these  brackets,  the 
manufacturers  proportion  them  so  that  the  distance  of  the  shaft 
from  the  wall,  called  the  extension  of  the  bracket,  may  be  varied  a 
1  sufficient  number  of  inches  either  way  from  the  nominal  value  so 
as  to  meet  the  extensions  of  the  adjacent  sizes.  For  the  same 
reason  the  proportions  for  each  nominal  extension  of  bracket, 
which  vary  with  the  diameter  of  the  shaft  to  be  supported  are  taken 
suitable  for  a  certain  maximum  diameter  of  shaft  and  the  bracket 
used  for  the  several  diameters  of  shaft  next  smaller.  These 
considerations  determine  the  values  of  C,  D  and  E  in  the  following 
proportions  which  were  taken  from  the  catalogue  of  a  prominent 
maker  and  which  apply  to  the  key-drawing.  Fig.  43.  In  these  pro- 
portions, A  is  the  diameter  of  the  shaft  to  be  supported;  B  is  the 
nominal  extension  of  the  bracket;  E  is  the  diameter  of  the  holding 
bolts  for  the  bearing,  the  square  heads  of  which  are  placed  in,  and 
held  from  turning  by  the  sides  of  the  grooves  in  top  of  the  bracket, 
and  F  is  diameter  of  the  supporting  bolts. 


A 

B 

c 

D 

.E 

F 

G 

A 

B 

C 

E 

» 

E 

F 

G 

If 

12 

8 

4; 

f 

f 

3f 

12 

11 

ft 

1 

1 

18 

8 

4 

f 

1 

18 

11 

ft 

1 

1 

-• 

to 

24 

8 

4; 

I 

1 

to 

24 

11 

ft 

1 

If 

-. 

30 

8 

4 

I 

If 

30 

11 

6^ 

1 

If 

2* 

36 

8 

4; 

1 

u 

4£ 

36 

11 

f>i 

1 

u 

] 

2f 

12 

10 

55 

1 

1 

4f 

18 

10 

5' 

1 

18 

12 

7| 

If 

If 

ti 

to 

24  ; 

10 

B 

1 

If 

to 

24 

12 

7^ 

If 

if 

If 

30 

10 

5| 

1 

If 

30 

12 

7J 

u 

i! 

li 

3* 

36 

10 

5| 

U 

If 

5? 

H  =  E  +  i". 
I    =  HE+- 

-  IE. 

=  I  +2 
L  =  E  + 
M=  E  —  \ 


N  =  B  +C. 
O    =  2F. 
P    =  2F  +M. 
Q   =  K  +  3  F. 
R  =  Q  +  3  F. 
S   =  P  +  2  F. 


T  =  F  +  r. 

u  =  ID. 

V  =  2F+i". 
W  =  4F. 
X  =  \G. 


32.  Wall  Box  Frames. — When  it  is  necessary  to  have  a  bearing 
where  a  shaft  passes  through  a  wall,  a  wall  box  frame,  Fig.  44,  is  set 
in  the  wall  to  support  the  bearing,  which  is  fastened  to  it  by  means 
of  bolts  or  studs.  This  frame  may  be  provided  with  wedges  for 


SHAFT  FIXTURES 


59 


vertical  alignment  of  the  shaft  as  shown  in  Fig.  44,  or  the  bearing 
may  be  bolted  directly  to  the  bottom  of  the  frame   as  indicated  in 


FIG.  44. 

the  key  drawing,  Fig.  45,  to  which  the  following  description  and 
empirical  proportions  apply.  The  raised  strips  on  the  inside  of  the 
bottom  of  the  frame  are  to  provide  the  necessary  finished  surface 
for  contact  with  the  finished  portion  of  the  bottom  surface  of  the 
base  of  the  bearing  without  machining  the  entire  surface.  Since 
each  size  of  frame  takes  several  sizes  of  bearings  the  width  of  these 
finished  strips  must  be  sufficient  to  permit  the  finished  portions 
extending  across  the  ends  and  center  of  any  size  of  bearing,  within 
the  range  used  with  this  frame,  to  rest  wholly  on  the  strips  when  at 


-E 


FIG.  45. 

the  extreme  points  of  sidewise  adjustment  in  either  direction. 
Should  there  be  a  considerable  space  between  the  outer  and  center 
strips  in  any  frame  additional  intermediate  strips  may  be  placed 
there  to  furnish  a  support  to  the  bearing  along  the  edge  of  the  base. 
The  sizes  of  these  frames  are  designated  by  numbers,  each  num- 
ber serving  for  sizes  of  bearings  as  follows : 


60 


SHAFT  FIXTURES 


Frame  Number. 

i 

2 

3 

4 

5 

6 

H 

2f 

3f 

4f 

6 

7 

Diameter  of  Shaft. 

to 

to 

to 

to 

to 

to 

In  general  they  must  be  designed  with  reference  to  the  particu- 
lar form  of  bearing  they  are  to  support.  The  proportions  here 
given  were  determined  for  use  with  the  babbitted  bearing  described 
in  article  27  on  page  50. 

A    =  maximum  diameter  of  shaft  to  be  used  in  frame. 

B    =  2JA  +  2i". 

C    =  2fA  +  7". 

D    =  f  A. 

E 

F 

G 

H 

K 

L 


+ 

E  +  I". 

IB. 


=  JC  =  width  of  frame. 

=  distance  between  holding  bolts  for  bearing  (see  article  27)  . 

33.  Hangers.  —  When  the  bearing  is  to  be  supported  from  above, 
the  intermediate  member  takes  the  form  of  a  drop  hanger,  Fig.  46, 
which  receives  a  bearing  of  the  type  shown  in  Fig.  36  (e)  on  page 


FIG.  46. 


SHAFT  FIXTURES  61 

47.  Horizontal  adjustment  is  provided  by  the  elongated  holes 
for  the  bolts  at  the  top  of  the  hanger  and  vertical  adjustment  is 
secured  from  the  pivot  screws  shown  above  and  below  the  bearing. 
The  drop  hangers  are  carried  in  stock  with  different  amounts  of 
drop  increasing  by  2"  intervals  from  8"  up  to  24"  and  by  6" 


FIG.  47.  W\ 

intervals  from  that  to  36"  except  that  shafts  above  3"  in  diameter 
require  more  than  the  minimum  drop  of  8".  An  adaptation  of 
these  hangers  for  attaching  to  a  post  is  shown  in  Fig.  47.  These 
post  hangers  provide  no  variation  of  the  distance  of  the  shaft  from 
the  post.  At  the  left  of  each  figure  may  be  seen  the  brace  links 
which  may  be  removed  so  that  the  shaft  may  be  dismounted 
without  removing  the  hanger  from  its  fastenings. 


CHAPTER  VI. 


TRANSMISSION  MEMBERS. 

34.  General  Statement. — In  this  chapter  are  considered  some 
of  those  machine  parts  which  are  usually  attached  to  revolving 
shafts.     These  include  such  members  as  pulleys,  gears,  cams,  etc. 
Their  adjacent  members  such  as  belts  and  cam  followers  are  briefly 
mentioned.     No  attempt  has  been  made  to  carry  the  discussion 
beyond  the  information  needed  for  the  drawings  of  a  brief  course 
in  Empirical  Design. 

35.  Pulleys. — The  use  of  pulleys  either  keyed  to  shafts  for  the 
purpose  of  transmitting  power  or  running  loose  on  shafts  for  the 
purpose  of  guiding  or  supporting  belts  is  too  common  to  require 
any  description.     Pulleys  are  usually  made  of  cast  iron,  of  wood,  of 
stamped  steel  or  of  combinations  of  these  materials.     They  are 
made  both  solid  and  split.     Split  pulleys  consist  of  two  equal  halves 
bolted  together  at  hub  and  rim.     Otherwise  the  proportions  are 
the  same  as  for  solid  pulleys.     Driving  pulleys  and  those  under 
heavy  loads  should  be  keyed  to  the  shaft.     Those  under  light  loads 
may  be  secured  to  the  shaft  by  means  of  set  screws  or  the  compres- 
sion of  bushings. 

There  is  a  wide  variation  in  the  diameters  of  shafts  upon  which  a 
pulley  of  any  nominal  size  (outside  diameter)  may  be  used.  The 
hubs  are  made  large  enough  for  the  largest  probable  diameter  of 
shaft.  In  solid  pulleys,  and  in  split  pulleys  which  are  to  be  keyed 
to  the  shaft,  the  hubs  are  bored  and  the  keyways  cut  to  order 
before  shipping  from  the  factory.  Split  pulleys  which  are  to  be 
secured  by  the  compression  of  bushings  have  their  hubs  already 
bored  to  receive  the  largest  diameter  of  shaft.  For  shafts  of  smaller 
diameters  split  bushings  are  supplied  to  make  the  necessary  reduc- 
tion. Such  pulleys  and  a  supply  of  bushings  are  usually  carried  in 
stock  by  dealers. 

The  stock  sizes  vary  to  some  small  extent  with  different  makers. 
In  general  they  vary  by  1"  from  6"  to  36"  in  diameter  and  by  2" 
from  36"  up  to  144".  The  widths  of  face  vary  by  1"  from  3"  up  to 


TRANSMISSION  MEMBERS 


63 


12"  and  by  2"  from  12"  up  to  60".  The  minimum  stock  width 
increases  from  3"  for  pulleys  36"  and  less  in  diameter,  up  to  12" 
for  112"  and  over  in  diameter.  The  maximum  width  of  face  in- 
creases from  12"  for  pulleys  6"  and  7"  in  diameter,  up  to  60"  for 
pulleys  96"  and  over  in  diameter.  When  the  hubs  are  bored  and 
the  keyways  cut  to  order  the  width  of  face  may  be  reduced  from  the 
nearest  stock  size  to  any  desired  width  at  a  slight  added  expense. 
Obviously  any  change  from  a  stock  diameter  will  require  building 
entirely  to  order  at  a  correspondingly  increased  cost. 

The  arms  of  pulleys  are  usually  elliptical  in  cross  section.     The 
arms  of  very  large  cast  iron  pulleys  are  tapered  both  in  width  and 


FIG.  48. 

thickness,  those  of  smaller  pulleys  in  width  only.  The  amount  of 
taper  in  width  varies  from  J"  to  f"  per  foot  per  side,  and  in  thick- 
ness from  |"  to  3^"  per  foot  per  side.  The  thickness  of  pulley  arms 
is  made  from  0.4  to  0.5  the  width.  The  wider  pulleys  are  made 
with  a  double  set  of  arms  to  sustain  the  rim.  Some  pulleys  not  so 
wide  in  proportion  to  their  diameters  are  made  with  either  single 
or  double  sets  of  arms.  In  addition  to  the  bore  of  the  hub  and  the 
face  of  the  rim  the  ends  of  the  hub  and  the  edges  of  the  rim  are 
finished. 

The  following  proportions  for  cast  iron  pulleys  having  six  arms 
apply  to  the  key  drawing,  Fig.  48,  when  all  dimensions  are  in 
inches. 

A    =  diameter  of  shaft. 
B    =  diameter  of  pulley. 


64  TRANSMISSION  MEMBERS 

C    =  width  of  face  =  1J  width  of  belt. 
D    =  f  \|  B  X  C  for  single  belts, 

=  T*  \!  B  X  C  for  double  belts. 
E    =D  —  TsB  to  D  —  sVB. 

F    =   JE  (taken  to  next  larger  •£>"  for  values  less  than  £"). 

G    =  jp'  per  foot  width  of  face.     (This  is  an  average  value.     The 

crown  is  made  greater  on  narrow  pulleys  and  less  on  wide 

ones.) 

H    =  f  C,  (This  is  an  average  value.    H  should  be  greater  for 

loose  than  for  tight  pulleys). 

=  f  C  +  ^B  + 1".  (This  gives  good  values  for  tight  pulleys.) 
J     =  A  +  f  D  but  not  to  exceed  If  A  +  J". 
K    =    diameter  of  set  screw 

=  TQ  ( J  —  A)  +  A"  when  bearing  on  shaft, 
=  width  of  key  when  bearing  on  key. 
L    =   2K. 
M  =  JK. 
N    =  1|  K. 

The  following  equations  give  satisfactory  radii  for  drawing  the 
several  curved  surfaces  but  should  not  be  given  as  dimensions. 


FIG.  49. 

For  the  crown  of  the  pulley  R  =  C  -r-  8G.  For  the  ellipse  of  the 
arms,  Fig.  49,  r,  =  f  the  major  axis,  r,  is  found  by  trial  to  past 
through  the  extremities  of  the  major  axis  and  tangent  to  the  arcs 
of  radius  r,. 

36.  Belts. — The  discussion  in  this  article  will  be  confined  to 
belts  of  flat  cross  section  such  as  would  be  used  on  pulleys  having 
rims  of  the  general  form  shown  in  Fig.  48.  Belts  may  be  made  of 
leather,  of  cotton,  of  rubber,  or  of  combinations  of  these  materials. 


TRANSMISSION  MEMBERS  65 

The  ends  of  the  belt  are  fastened  together  as  smoothly  as  practic- 
able, forming  a  closed  loop  which  is  passed  tightly  over  the  faces 
of  two  or  more  pulleys.  Its  ability  to  transmit  power  is  dependent 
upon  the  tightness  of  the  belt  on  the  driving  and  driven  pulleys, 
upon  the  friction  between  the  belt  and  the  pulleys,  and  upon  the 
area  of  cross  section  of  the  belt.  In  commercial  belting  the  stock 
sizes  of  cross  sections  vary  both  in  width  and  in  thickness. 

Leather  Belting. — The  different  thicknesses  of  leather  belting 
are  obtained  by  cementing  together  two  or  more  thicknesses  of 
leather.  Such  belting  is  known  as  single,  double,  triple  and 
quadruple  leather  belting  according  to  the  number  of  thicknesses 


FIG.  50.  ' 

used.  Single  belting,  A"  to  J"  thick,  and  double  belting,  A"  to 
•fs"  thick,  are  the  thicknesses  commonly  used.  The  standard 
widths  of  leather  belting  are, 

J"  to  1"  varying  by  J";  1"  to  28"  varying  by  1"; 

1"  to  4"  varying  by  }";  28"  to  40"  varying  by  2"; 

4"  to  7"  varying  by  }";  40"  to  72"  varying  by  4". 

The  following  empirical  equations  give  good  values  for  the  power 
which  may  be  transmitted  by  leather  belts  having  effective  tensions 
of  38  pounds  and  60  pounds  per  inch  of  width  for  single  and  double 
belts  respectively,  at  speeds  not  exceeding  1,000  feet  per  minute. 
D    =•  diameter  of  pulley  in  niches. 
N    =   revolutions  per  minute  of  pulley. 
W  =  width  of  belt  in  inches. 
H.P.  =  horsepower  transmitted 

WDN          . 

=  for  single  belts, 

3,300 

WDN 

=  for  double  belts. 

2,100 

37.    Handwheels. — A  handwheel  is  used  in  the  place  of  a  crank 
or  wrench  in  places  where  it  is  desirable  to  be  able  to  grasp  with  the 


66 


TRANSMISSION  MEMBERS 


same  ease  and  force  in  all  phases  of  a  rotation.  The  handwheel 
consists  of  a  hub  and  spokes  of  the  form  usual  to  pulleys,  and  a  rim 
of  such  form  as  to  readily  fit  the  hand.  The  rim  is  most  frequently 


FIG.  51. 

circular  in  section  or  modified  as  in  Fig.  50(a)  to  afford  an  easier 
grip  for  the  larger  sizes.  The  U.  S.  Navy  uses  a  rectangular  form 
with  the  corners  slightly  rounded  in  its  smaller  sizes  and  modified 
to  the  form  of  Fig.  50(b)  in  its  larger  sizes.  Small  sizes  may  be 
finished  all  over  but  in  the  larger  sizes  the  rim  and  ends  of  the  hub 
alone  are  finished.  The  spokes  or  arms  are  usually  straight  but 
may  be  curved  as  in  Fig.  51  to  relieve  stresses  due  to  shrinkage  in 


FIG.  52. 


TRANSMISSION  MEMBERS 


67 


casting.     The  most  common  cross  section  is  in  the  form  of  an 
ellipse. 

Handwheels  are  not  carried  in  stock  and  no  standard  propor- 
tions can  be  given.  The  nominal  size  is  the  outside  diameter  of  the 
rim.  Table  XIV  gives  good  values  for  the  dimensions  shown  in  the 
key  drawing,  Fig.  52,  for  the  6"  and  16"  sizes.  Values  for  these 
dimensions  for  other  sizes  from  4"  to  24"  may  be  obtained  by  the 
graphical  method  described  in  article  3  on  page  5,  using  a  straight 
line  for  the  curve  in  each  case. 

TABLE  XVI. 
PROPORTIONS  FOR  CAST  IRON  HANDWHEELS. 


A 

B 

c 

D 

E 

F 

G 

H 

K 

T 

6 
16 

ll 

li 

2* 

I 

1 

a 

i 

1 

A 

i 

38.     General  Nature  and  Properties  of  Gears. — A  gear  consists 
primarily  of  a  hub  and  arms,  similar  to  those  for  pulleys,  which 


support  a  rim  upon  the  surface  of  which  teeth  are  formed.  These 
teeth  interlock  with  the  teeth  of  a  mating  gear,  Fig.  53,  to  transmit 
the  power.  Where  one  of  these  gears  has  a  small  number  of  teeth 
it  is  known  as  a  pinion.  There  is  an  imaginary  smooth  surface 
passing  through  the  teeth  of  each  gear  at  approximately  their 
mid-height  which  rolls  upon  the  corresponding  surface  of  the  mat- 


68  TRANSMISSION  MEMBERS 

ing  gear.  These  imaginary  surfaces  are  called  the  pitch  surfaces 
of  the  gears.  Gears  may  be  classified  in  a  general  way  according 
to  the  forms  of  their  pitch  surfaces.  Spur  gears,  Fig.  53 (a),  have 
cylinders  for  pitch  surfaces;  bevel  gears,  Fig.  53 (b),  have  conical 
frustums  for  pitch  surfaces;  and  worm  gears,  Fig.  53 (c),  have 
pitch  surfaces  of  double  curvature.  A  pair  of  equal  bevel  gears 
with  shafts  perpendicular  are  called  mitre  gears. 

A  cross  section  taken  through  a  cylindrical  or  a  conical  pitch 
surface  is  a  circle,  called  the  pitch  circle  or  pitch  line.  Its  diameter 
is  called  the  pitch  diameter.  For  bevel  gears  the  pitch  circle  is 
taken  at  the  larger  end  of  the  frustum.  The  linear  distance  in 
inches  from  center  to  center  of  adjacent  teeth,  measured  along  the 
arc  of  the  pitch  circle,  is  known  as  circular  pitch.  The  ratio  of  the 
number  of  teeth  to  the  diameter  of  the  pitch  circle  in  inches  is  called 
diametral  pitch.  The  following  relations  are  obvious  from  the 
above  definitions: 

D    =  pitch  diameter  in  inches, 
N    =  number  of  teeth, 

N 
Pd  =  diametral  pitch  =^, 

7TD  TT 

pc  =  circular  pitch  =  —  =  — . 

N       pd 

39.  Proportions  for  and  Properties  of  Gear  Teeth.— The  force 
which  may  be  exerted  by  a  gear  tooth  upon  its  mating  tooth  is 
dependent  upon  its  thickness,  width,  and  height,  and  upon  its 
linear  velocity.  By  the  width  of  the  tooth  is  meant  the  distance, 
f,  across  the  face  of  the  gear  in  Fig.  54.  The  thickness  of  a  standard 
gear  tooth  at  the  pitch  line  is  one-half  the  circular  pitch  (approx- 
imate in  the  case  of  gears  having  cast  teeth).  The  height  of  a 

2" 
standard  gear  tooth  has  been  empirically  fixed  at   —  plus  an 

Pd 

0.157"  1" 

allowance  of   for  clearance.     Of  this  height    —  extends 

Pd  Pd 

outside  the  pitch  line  and  is  called  the  addendum.  Experiments 
by  Mr.  Wilfred  J.  Lewis  have  shown  that  owing  to  increasing 
shock,  the  allowable  working  fibre  stress  in  gear  teeth  decreases  as 


TRANSMISSION  MEMBERS 


69 


the  velocity  increases.  Table  XV  gives  values  of  allowable'fibre 
stresses  for  cast  iron  gear  teeth  for  various  linear  velocities  in  feet 
per  minute  at  the  pitch  line.  These  values  may  be  increased  2| 

times  for  steel. 

TABLE    XV. 
ALLOWABLE  FIBRE  STRESSES  IN  CAST  IRON  GEAR  TEETH. 


Velocity 
Stress. 

0-100 
8000 

200 
6000 

300 
4800 

600 
4000 

900 
3000 

1200 
2400 

1800 
2000 

2400 
1700 

His  experiments  showed  further  that  increasing  the  width  of  the 
tooth  beyond  three  times  the  circular  pitch  was  not  effective  in 
increasing  the  strength  of  the  tooth  although  widths  from  2jpc 
to  3|  pc  give  good  results.  These  proportions  may  be  summarized 
in  the  following  equations: 

I" 
a   =  addendum  = 

Pa 


h   =  total  height  of  tooth 


f  =  width  of  face  =  3  pc  = 


2.157" 

Pd 
9.42" 


=  0.687pc 


v     =  linear  velocity  in  feet  per  minute  at  the  pitch  line 
TT  +  D  +  R.P.M. 

12 

s  =  allowable  fibre  stress  in  pounds  per  square  inch  at  velocity, v; 
n     =  number  of  teeth  on  weaker  gear; 
W  =  safe  load  on  tooth  in  pounds 

=  spcf      I   0.124-  —          for  15°  involute  teeth,  and  for 

cycloidal  teeth  when  the  diameter  of  the  describing  circle 

equals  the  radius  of  the  12  tooth  pinion.     (Lewis.) 

The  teeth  of  gears  are  usually  machined  to  exact  size  and  form, 

in  blanks  prepared  for  the  purpose.     These  are  called  cut  teeth. 

If  the  teeth  are  large  the  amount  of  machining  is  reduced  by  casting 

to  approximate  form  with  proper  allowance  for  finishing.     It  is 

customary  in  making  drawings  for  cut  gears  to  draw  the  blanks 

without  teeth.     In  cross  section  views  the  height  of  the  tooth  is 


70 


TRANSMISSION  MEMBERS 


indicated  on  the  section  of  the  rim  without  cross  hatching,  as 
shown  in  Fig.  54.  The  number  and  form  of  the  teeth  and  their 
diametral  pitch  is  specified  in  a  note.  Some  large  gears  for  rough 
work  may  have  their  teeth  cast  to  form  as  closely  as  possible  and 
be  used  without  machining.  Such  gears  are  said  to  have  cast 
teeth,  and  drawings  for  them  should  show  the  teeth  in  detail  fully 
dimensioned.  The  number  of  teeth  and  circular  pitch  is  given  in  a 
note. 

40.  Materials  used  in  Gears. — The  material  most  commonly 
used  for  gears  is  cast  iron.  Because  of  the  greater  amount  of  wear 
upon  their  teeth,  pinions  to  work  with  cast  iron  gears  are  frequently 


made  of  steel.  The  same  relative  equalization  of  wear  may  also 
be  obtained  by  making  the  teeth  of  the  gear  of  hard  wood  mortised 
into  the  cast  iron  rim.  Such  gears  are  known  as  mortise  gears. 
When  gears  are  run  at  high  speeds  the  noise  may  be  greatly  de- 
creased by  making  the  pinion  of  rawhide,  fibre,  or  cloth  tightly 
compressed  between  cast  iron  or  steel  plates  at  the  sides. 

41.  Proportions  for  Spur  Gears. — Very  small  spur  gears  or 
pinions  are  made  solid  without  distinction  between  hub  and  rim. 
Gears  of  sufficient  size  so  that  the  normal  hub  and  rim  would  be 
separated  but  having  less  than  36  teeth  are  made  with  a  continuous 
web  in  the  place  of  arms.  Gears  having  from  36  to  60  teeth  have 
four  arms.  Those  having  more  than  60  teeth  should  have  six  arms 
except  in  the  case  of  very  large  gears  which  may  have  from  eight 


TRANSMISSION  MEMBERS  71 

to  twelve  arms.  The  usual  cross  sections  for  the  arms  of  spur  gears 
are  elliptical,  Fig.  54 (a),  or  in  the  shape  of  a  cross,  Fig.  54(b). 
These  arms  are  tapered  f "  per  foot  per  side  in  width  and  the 
thickness  of  elliptical  arms  is  usually  made  one-half  of  the  width. 
In  small  gears  the  thickness  of  elliptical  arms  may  be  made  uniform 
at  an  average  value. 

The  following  proportions  are  for  cast  iron  spur  gears  having  six 
arms  and  apply  to  the  key  drawings,  Fig.  54,  when  all  dimensions 
are  in  inches.  In  dimensioning  drawings  for  these  gears  the  out- 
side diameters  and  pitch  diameters  should  be  given  as  decimals, 
unless  the  exact  value  can  be  otherwise  expressed. 

A  =  diameter  of  bore. 

D  =  pitch  diameter. 

pd  =  diametral  pitch. 

pc  =  circular  pitch, 

f  =  width  of  face, 

n  =  number  of  teeth. 

,   D  5       D  ,    n  -f-  250 

B    =  A+1.6Pc+-  =  A  + 


50  Pd  50  Pd 


f  +  — . 

40 


E    =  2J  pc  = =  width  of  arm  at  pitch  line. 

Pd 

F    =  JE  =  thickness  of  arm  at  pitch  line. 

K'A/t" 

GT^V              •*      t~*>r\  *•                           TV           t/«T*ty 
=  D  -  1.735  pc  =  D- 


Pd 

H  =  JF. 
J     =  H. 

7  22" 
K    =  2.3  pc  =  — =  width  of  arm  at  pitch  line. 

Pd 
L    =  f  -  2  R. 

1  17" 

M  =  J  pc  =   — . 


N  =   0.3  pc  = 


Pd 
0.94" 

Pd 


TRANSMISSION  MEMBERS 


O    =  }K 
P    =  O. 
B,    =  M. 

Taper  of  arms  =  f "  per  foot  per  side  in  width. 

42.  Proportions  for  Bevel  Gears. — Bevel  gears  may  be  designed 
for  use  on  shafts  intersecting  at  any  desired  angle  but  that  angle  is 
usually  90°.  Very  small  bevel  gears  or  pinions  may  have  the  hub 
and  rim  solid.  Gears  somewhat  larger  have  a  continuous  web 


FIG.  55. 

joining  the  rim  to  the  hub  with  broad  stiffening  ribs,  Fig  55,  to 
resist  the  side  pressure.  In  large  bevel  gears  these  stiffening  ribs 
are  placed  opposite  the  middle  of  each  arm  giving  it  a  T  section. 
Bevel  gears  should  be  so  laid  out  that  as  few  of  the  dimensions  as 
possible  shall  need  to  be  in  decimals  and  at  the  same  time  to  avoid 
decimal  dimensions  on  adjacent  members.  This  may  be  best 
accomplished  by  making  the  distance  from  the  finished  surface  at 
the  back  of  the  hub  to  the  apex  of  the  conical  pitch  surface  an 
amount  which  will  not  involve  a  decimal.  The  distance  from  this 
surface  to  the  outer  points  of  the  teeth,  the  outside  diameter  and 
the  pitch  diameter  are  then  the  only  dimensions  which  need  to 
be  expressed  in  decimals  for  cut  teeth.  If  the  teeth  are  to  be  cast 
j.he  radii  used  in  laying  out  the  approximate  tooth  profiles  should 


TRANSMISSION  MEMBERS  73 

also  be  given  as  decimals.  The  angles  which  the  faces  of  the  teeth 
and  the  edges  of  the  rim  make  with  a  plane  perpendicular  to  the 
shaft  should  be  given.  These  angles  are  called  the  face  angle  and 
edge  angle  respectively.  The  angles  and  the  decimal  dimensions 
should  be  computed. 

The  following  equations  which  apply  to  the  key  drawing,  Fig.  55, 
give  good  proportions  for  cast  iron  bevel  gears  when  all  dimensions 
are  in  inches. 

d     =  pitch  diameter.  * 

pc    =  circular  pkch. 
pd   =   diametral  pitch. 

A  =  width  of  face  =  3pc-J"  =  ^—  \n ',    but  not  to  exceed 

.    Pd 
one-third  the  length  of  element  of  pitch  cone. 

B    =  length  of  hub   =   A  -f  —  (for  gears), 

20 

n  78" 

=   A  +  ^  =  A  +—  -(for  pinions). 

4  Pa 

C    =  bore  of  hub. 
D    =  diameter  of  hub  =  IfC  +  (i"to  \"). 

1  53" 

E    =  thickness  of  metal  in  arms  or  web  =  .48  pc  =  — 

Pd 
F    =   distance  from  bottom  of  tooth  to  face  of  web  or  arm 

1.41" 

=  .45  pc  =        — . 

Pd 
(Used  only  in  laying  out  and  not  given  on  drawing.) 

r^            A  -j     j-                     i    •    2  cos  8 
G    =  outside  diameter  =  d  H £ 


FIG.  56. 

43.  Worm  Gears. — The  worm,  shown  at  the  top  in  Fig.  53 (c), 
is  the  driving  member.  A  cross  section  through  the  screw  thread 
of  a  standard  worm  is  shown  in  Fig.  56.  The  following  equations 


74 


TRANSMISSION  MEMBERS 


apply  to  the  key  drawings,  Fig.  56  and  57,  and  give  the  usual 
proportions  for  steel  worms  working  with  cast  iron  gears.  All 
dimensions  are  in  inches. 


d 

P 
a 
h 
n 
L 
T 

R 

A 
B 


FIG.  57. 

=  pitch  diameter  of  worm. 
=   linear  pitch. 
=  addendum  =  0.3183  p. 
=  depth  of  thread  =  0.6866  p. 
=  number  of  threads  in  worm. 
=  lead  of  worm  =  n   X  p. 
=   number  of  teeth  in  worm  wheel. 

T 

=  velocity  ratio  of  worm  to  wheel   =  - 

n' 

=  bore  of  wheel. 

=  diameter  of  hub  =  If  A  -f  (f "  to  }"). 


C   =  length  of  hub  =  H  -h 


or  to  suit. 


TRANSMISSION  MEMBERS  75 

D    =  pitch  diameter  of  wheel. 

E    =  throat  diameter  of  wheel   =   D  +  2a. 

F    =  outside  diameter  of  wheel  (un trimmed)  =  E  +2G(l-cos~). 

2 

G    =  throat  radius  of  wheel  =  JP  —  2a. 

H    =  width  of  face  of  wheel  =  P  sin  -  +  (f"  to  J"). 

J  =  thickness  of  web  =  0.48  p. 

K  =  thickness  of  rim  =  0.48  p. 

M  =  bore  of  worm  in  inches. 

N  =  root  diameter  of  worm  =  P  -  2h. 

P  =  outside  diameter  of  worm. 


Q    =  minimum  length  of  thread  on  worm  =  \/  E2  -  (E  -  4a  )2. 

a     =  face  angle  of  wheel. 

/3    =  gashing  angle  =  helix  angle  of  worm. 


44.  Commercial  Gears.  —  The  demand  for  gears  is  so  varied  that 
it  is  not  feasible  for  the  manufacturers  to  attempt  to  carry  in  stock 
gears  to  meet  all  conditions.  This  is  especially  true  for  other  than 
cast  iron  spur  gears  with  cut  teeth.  Such  gears,  completely 
finished,  are  carried  in  stock  by  some  makers  in  several  of  the  more 
commonly  used  pitches  and  with  enough  different  numbers  of 
teeth  to  meet  most  needs.  The  pitches  most  commonly  carried 
are  8,  12,  16,  20  and  24.  The  numbers  of  teeth  vary  by  somewhat 
irregular  intervals  from  12  up  to  150  or  more.  Considerably  fewer 
sizes  of  cast  iron  bevel  gears  with  cut  teeth,  in  pairs,  for  shafts  at 
90°,  are  also  carried  in  stock.  These  include  mitre  gears  in  numer- 
ous pitches  from  4  to  32  and  gears  with  velocity  ratios  from  3  :  2  to 
4  :1  in  three  or  four  different  pitches.  Finished  spur  and  bevel  gears 
with  cast  teeth  are  carried  in  somewhat  larger  pitches  and  less 
variety  of  numbers  of  teeth.  Very  small  spur  and  bevel  gears 
and  worm  wheels  of  brass  are  also  carried.  While  this  statement 
gives  a  general  idea  of  what  may  be  obtained  exact  information 
must  be  secured  from  the  catalogs  of  the  individual  makers. 
Wherever  it  is  feasible  to  use  these  finished  stock  gears  a  consider- 


76 


TRANSMISSION  MEMBERS 


able  saving  in  expense  is  effected.  No  changes  from  stock  dimen- 
sions may  be  made,  however,  except  as  to  bore  of  hub  and  that  at  an 
added  cost. 

Patterns  for  spur  gears  of  any  desired  pitch  and  number  of 
teeth,  and  for  pairs  of  bevel  gears  of  any  pitch  and  velocity  ratio, 
are  usually  carried  in  stock.  Gears  from  these  patterns  may  be 
quickly  cast  to  order.  Finished  patterns  for  spur  and  bevel 
mortise  gears  are  carried  in  stock  by  some  manufacturers  in  some- 
what fewer  sizes. 

45.  Cams. — Cams  are  not  carried  in  stock  commercially.  The 
sizes  in  Table  XVI  are  given  by  Guldner  for  gas  engine  cams  having 


FIG.  58. 

hardened  steel  rolls,  carrying  a  load  not  to  exceed  3000  pounds  per 
inch  of  length.  In  the  absence  of  other  proportions  these  may  be 
used  for  disk  cams  in  general  within  the  range  of  sizes  given. 
When  the  diameter  of  cam  shaft  is  V  or  less  the  diameter  of  roll 
may  be  made  Ij  times  the  diameter  of  ;;haft. 

The  other  dimensions  shown  in  the  key  drawing,  Fig.  58,  may  be 
taken  as  given  by  the  equations  below.  All  dimensions  are  in 
inches. 

diameter  of  hub  or  boss  =  If  A  +  i". 


B 
C 
D 


length  of  hub  =  A  to  2  A. 

least  radius  of  cam  or  radius  of  base  circle 

|B  +  (jV  to  J").     This  may  be  made  larger  if  conditions 

require  a  larger  cam. 


TRANSMISSION  MEMBERS 


77 


H*may  be  made  to  suit  or  may  be  omitted  entirely.  The  face  of 
the  cam  is  usually  made  a  little  wider  than  the  length  of  the  roll. 
The  roll  is  preferably  carried  in  a  forked  end,  but  it  may  be  offset 
if  necessary  to  save  space. 


TABLE    XVI. 
GAS  ENGINE  CAMS  AND  ROLLS. 


Length  of  Roll. 


FIG.  59. 


The  following  equations  give  good  proportions  for  the  stamp  mill 
cam  and  its  tappet  shown  in  Fig.  59  (a)  and  (b), 


78  TRANSMISSION  MEMBERS 

A  =   diameter  of  cam  shaft. 

B  =  £{  A. 

c  =  HA. 

D  =  }  A. 

E  =JD. 

F  =  1J  E. 

G  =A. 

H  =i  A. 

J  =  I  A. 

K  =  diameter  of  stamp  stem. 

L  =  3  K. 

M  =  3i  K. 

N  =  f  K. 

O  =  2  K 

P  =  If  K 


CHAPTER  VII. 


PIPE  AND  PIPE  FITTINGS. 

46.  Varities  of  Pipe. — Pipe,  made  from  various  materials  such 
as  wood,  tile,  cast  iron,  wrought  iron,  steel,  lead,  brass,  etc.,  is  kept 
in  stock  by  manufacturers.     The  processes  by  which  each  of  these 
is  formed  vary  widely.     They  include  casting  in  a  mold;  squirt- 
ing through  a  hole  partially  closed  by  a  mandrel;  forcing  a  mandrel 
through  a  solid  billet  of  metal;  bending  and  welding  the  edges  of  a 
strip  of  metal;  and  bending  and  riveting  the  edges  of  a  sheet  of 
metal.     The  discussion  in  this  book  will  be  confined  to  wrought 
iron  and  steel  pipe  formed  by  bending  and  welding. 

47.  Wrought  Iron  and  Steel  Pipe. — Pipe  made  from  steel  has 
very  largely  replaced  wrought  iron  pipe  for  the  conveying  of 
water,  gas  and  steam.     Wrought  iron  remains  in  use  chiefly  in 
those  places  where  resistance  to  corrosion  is  a  determining  factor. 
The  terms  "wrought  iron"  and  "steel"  are  used  so  indiscriminately 
in  this  connection  that  a  positive  statement  is  necessary  wherever 
either  would  not  be  acceptable.     Steel  is  usually  supplied  when 
not  otherwise  specified.     The  methods  of  manufacturing  these  two 
are  very  similar.     The  metal  is  rolled  into  strips  of  the  correct 
thickness  for  the  pipe  and  of  a  width  which  will  bend  into  a  tube 
with  sufficient  allowance  for  welding.     The  small  diameters  of 
pipe  are  butt  welded  while  larger  diameters  are  lap  welded.     The 
ends  are  trimmed  back  as  far  as  necessary  to  remove  all  imperfectly 
welded  portions  and,  on  standard  pipe  12"  and  less  in  diameter, 
threaded.     An  additional  charge  is  made  for  threading  extra  weight 
or  large  diameter  pipe. 

Four  thicknesses  or  weights  of  pipe  12"  and  less  in  diameter  are 
made.  These  are  commercially  known  as  merchant,  card  or  full 
weight,  extra  strong  and  double  extra  strong  pipe.  The  term 
"standard"  is  applied  by  some  to  full  weight  pipe  and  by  others 
to  merchant  pipe.  Merchant  pipe  is  generally  understood  unless 
otherwise  specified  but  great  care  must  be  taken  when  using  the 
term.  The  inside  diameter  of  the  card  or  full  weight  pipe  roughly 

79 


80 


PIPE  AND  PIPE  FITTINGS 


approximates  the  nominal  size.  The  outside  diameter  for  any 
nominal  size  is  made  the  same  for  each  weight  so  that  the  same 
fittings  and  threading  machinery  may  be  used.  The  proportions 
for  the  commercial  sizes  of  wrought  iron  and  steel  pipe  and  the 
standard  threading  for  each  are  given  in  Table  XVII.  The  pro- 
portions for  merchant  pipe  differ  so  little  from  those  for  full  weight 
pipe  that  no  different  values  are  listed  by  the  manufacturers.  The 

TABLE  XVII. 
WROUGHT  IRON  AND  STEEL  PIPE  AND  PIPE  THREADS. 


DIAMETERS 

AREAS  • 

THREADS 

Actual  Inside 

Inside 

a 
v  a; 

p 

II 

^S*| 

ii 

| 

o  g  bo 

3J 

bo 

ri 

rt 

a 

§ 

*£  i*£ 

o 

§ 

| 

IbO 

§ 

c 

0 

40 
K 

W  bo 

I 

el 

tffi 

1 

3 

i 

•3 

s 

|| 

i 

C/D 

s 

|l 

1 

11 

|a 

||l 

fc 

< 

£ 

W 

QW 

h 

W 

P 

* 

3l 

0.405 

0.270 

0.205 

0.057 

0.033 

27 

0.334 

0.19 

. 

0.540 

0.364 

0.294 

0.104 

0.068 

18 

0.433 

0.29 

0.675 

0.494 

0.421 

0.191 

0.139 

18 

0.568 

0.30 

0.840 

0.623 

0.542 

0.244 

0.304 

0.231 

0.047 

14 

0.701 

0.39 

1.050 

0.824 

0.736 

0.422 

0.533 

0.425 

0.140 

14 

0.911 

0.40 

1 

1.315 

1.048 

0.951 

0.587 

0.861 

0.710 

0.271 

iu 

1.144 

0.51 

ji 

1.660 

1.380 

1.272 

0.885 

1.496 

1.271 

0.615 

ill 

1.488 

0.54 

ji 

1.900 

1.610 

1.494 

1.088 

2.038 

1.753 

0.930 

1.728 

0.55 

22 

2.375 

2.067 

1.933 

1.491 

3.356 

2.935 

1.744 

nl 

2.201 

0.58 

2* 

2.875 

2.468 

2.315 

1.755 

4.780 

4.209 

2.419 

8 

2.619 

0.89 

3 

3.500 

3.067 

2.892 

2.284 

7.388 

6.569 

4.097 

8 

3.241 

0.95 

4.000 

3.548 

3.358 

2.716 

9.887 

8.856 

5.794 

8 

3'.738 

1.00 

42 

4.500 

4.026 

3.818 

3.136 

12.730 

11.449 

7.724 

8 

4.234 

1.05 

41 

5.000 

4.508 

4.280 

3.564 

15.961 

14.387 

9.976 

8 

4.731 

.10 

5 

5.562 

5.045 

4.813 

4.063 

19.990 

18.193 

12.965 

8 

5.290 

.16 

6 

6.625 

6.065 

5.751 

4.875 

28.886 

25.976 

18.665 

8 

6.346 

.26 

7 

7.625 

7.023 

6.625 

5.875 

38.743 

34.472 

27.109 

8 

7.340 

.36 

8 

8.625 

7.982 

7.625 

6.875 

50.021 

45.664 

37.122 

8 

8.334 

.46 

9 

9.625 

8.937 

8.625 

62.722 

58.426 

8 

9.327 

1.57 

10 

10.750 

10.019 

9.750 

78.822 

74.662 

8 

10.445 

1.68 

11 

11.750 

11.000 

10.750 

95.034 

90.764 

8 

11.439 

1.78 

12 

12.750 

12.000 

11.750 

113.098 

108.430 

8 

12.433 

1.88 

14 

14.000 

13.250 

137.887 

8 

13.675 

2.00 

PIPE  AND  PIPE  FITTINGS 


81 


mill  lengths  usually  approximate  to  24  feet  but  may  include  pieces 
as  short  as  12  feet.  A  small  extra  charge  is  made  for  pipe  cut  to 
specified  lengths.  This,  however,  may  be  more  economical  when 
the  desired  lengths  are  know,  than  to  cut  the  pipe  on  the  job. 
Specify  nominal  size,  weight  and  length. 

In  pipe  14"  and  more  in  diameter  the  nominal  size  is  the  outside 
diameter.  This  is  commonly  known  as  outside  diameter  or  O.  D. 
pipe.  The  stock  sizes  vary  by  I"  up  to  22"  and  by  2"  from  22"  to 
30".  Such  pipe  is  made  in  thicknesses  varying  by  ^V  from  J"  to 
f"  for  sizes  up  to  20",  from  &"  to  f  "  up  to  22",  from  f "  to  f  "  up  to 
28"  and  from  A"  to  f "  for  30",  except  that  a  thickness  of  TT"  is 
not  made  in  any  of  the  diameters,  f "  and  \"  are  the  more  general- 
ly used  thicknesses.  Outside  diameter  pipe  is  generally  furnished 
with  plain  ends  and  random  lengths.  Mill  lengths  run  about  24 
feet.  Specify  nominal  size,  thickness  and  length. 

48.  Pipe  Threads. — Upon  the  recommendation  of  a  committee 
of  the  American  Society  of  Mechanical  Engineers  the  Briggs 
standard  of  pipe  threads  was  adopted  on  October  27,  1886,  by  the 
manufacturers  in  the  United  States  of  wrought  iron  pipe  for  gas, 


FIG.  60. 

steam  and  water.  The  change  to  steel  pipe  has  caused  no  change 
in  the  standard  used.  A  cross  section  through  the  Briggs  threads 
appears  in  the  longitudinal  section  of  pipe  shown  in  Fig.  60.  The 
sides  of  the  thread  section  make  an  angle  of  60°  with  each  other 
and  with  the  axis  of  the  pipe.  The  top  of  the  thread  and  the 
bottom  of  the  space  in  the  theoretical  form  are  rounded  slightly 
making  the  depth  0.8  of  the  pitch.  In  general  this  rounding  of  the 
corners  of  the  thread  is  not  obtained  in  practice  owing  to  difficulty 
in  grinding  the  cutting  tools.  A  sharp  V  form  at  the  root,  and  the 
point  cut  off  flat,  leaving  the  depth  0.833  of  the  pitch,  is  the  usual 
section  found.  The  thread  is  cut  on  a  taper  of  f  "  per  foot.  In 


82  PIPE  AND  PIPE  FITTINGS 

addition  to  the  threads  perfect  at  both  top  and  bottom  there  are 
two  effective  threads  imperfect  at  the  top  only.  Normally  the 
pipe  should  enter  the  fitting  a  distance  equal  to  the  length  of  per- 
fect thread.  The  two  additional  turns  provide  a  margin  in  case  of 
imperfect  fitting.  The  remainder  of  the  thread  is  not  of  full 
depth  and  does  not  enter  the  fitting.  The  following  equations  give 
the  complete  proportions  for  the  thread: 

D    =  outside  diameter  of  pipe; 

N    =  number  of  threads  per  inch; 

4.8"    _}_    0.8  D 
L    =  length  of  perfect  thread  =  — 


LI    =  length  of  effective  thread   = 


N 
6.8"  +  0.8  D 


N 

10.8"  +   0.8  D 
T    =    total  threaded  length    =   -       — i^r- 

The  values  of  D,  N  and  L  for  the  commercial  sizes  of  pipe  are 
given  in  Table  XVII  on  page  80. 

49.  Pipe  Joints. — There  are  two  general  types  of  pipe  joints. 
The  adjacent  ends  of  two  sections  of  pipe  may  be  screwed  into  a 
simple  threaded   sleeve,   called   a   coupling,   or  flanges   may   be 
attached  to  the  ends  of  the  sections  of  pipe  and  the  adjacent  flanges 
bolted  together.     The  former  of  these  types  is  very  much  used  for 
pipe  of  small  diameters  under  low  pressures. 

50.  Couplings. — These  couplings   are  made  of  wrought  iron 
with  right-hand  threads  for  all  standard  sizes  of  pipe  up  to  12" 
and  are  furnished  with  the  pipe  unless  it  is  ordered  flanged.     For  2" 
pipe  and  smaller,   couplings  of  malleable  iron  with  right-hand 
threads  are  carried  in  stock.     For  3"  pipe  and  smaller,  couplings  of 
malleable  iron  threaded  one  end  right-hand  and  the  other  end  left- 
hand  are  carried  in  stock.     For  all  couplings  the  nominal  size  is 
the  same  as  the  nominal  size  of  the  pipe  which  it  fits.     They  are 
carried  in  stock  either  black  or  galvanized.     Black  is  usually 
supplied    unless    otherwise    specified. 

51.  Pipe  Flanges. — The  most  common  type  of  pipe  flange  is 
that  shown  (with  a  section  cut  away)  in  Fig.  61.     These  flanges 
screw  on  the  ends  of  the  pipe.     Thin  rings  of  rubber,  asbestos,  or 


PIPE  AND  PIPE  FITTINGS 


83 


some  soft  metal  like  copper  or  lead,  are  placed  between  the  flanges 
before  bolting  together,  in  order  to  make  the  joint  tight.  These 
rings  are  called  gaskets.  The  pipe  should  extend  sufficiently 
through  the  flange  to  be  faced  off  even  with  the  face  of  the  flange 


FIG.  61. 

and  should  bear  on  the  gasket.  The  bolts  are  used  in  multiples  of 
four  and  are  equally  spaced  to  straddle  the  center  lines.  The  bolt 
holes  are  drilled  J"  larger  than  the  nominal  diameter  of  the  bolts. 
Formerly  there  were  two  recognized  systems  of  pipe  flanges  for 
different  pressures.  These  were  the  A.  S.  M.  E.  Standard  Pipe 
Flanges  for  pressures  up  to  125  pounds  per  square  inch  and  the 


FIG.  62. 


Manufacturers'  Standard  Pipe  Flanges  for  pressures  up  to  250 
pounds  per  square  inch.  Both  of  these  systems  are  being  super- 
seded by  the  American  or  United  States  Standard  Pipe  Flanges  for 
each  of  the  above  pressures.  These  two  weights  of  flanges  are 
known  respectively  as  standard  and  extra  heavy.  Values  for  the 
dimensions  indicated  in  Fig.  62  have  been  determined  for  nominal 
diameters  of  pipe  up  to  WO"  for  standard  flanges,  and  up  to 


84  PIPE  AND  PIPE  FITTINGS 

48"  for  extra  heavy  flanges.  The  values  of  these  dimensions 
and  the  numbers  and  sizes  of  bolts  for  each  weight  for  sizes  up  to 
48"  are  given  in  Table  XVIII.  When  the  diameter  of  the  bolt 
is  If"  or  over  stud  bolts  are  recommended.  Bolts  with  square 
heads  and  hexagon  nuts  are  recommended  for  smaller  sizes. 
Standard  flanges  32"  and  over  and  all  extra  heavy  flanges  are  spot 
bored  for  nuts.  On  all  extra  heavy  flanges  the  finished  face 
extends  out  to  within  y^"  from  the  inside  edge  of  the  bolt  holes. 
The  thickness  of  the  flanges  outside  this  point  is  reduced  y^"  in 
order  that  the  full  pull  of  the  bolts  may  be  exerted  in  compressing 
the  gasket  between  the  finished  faces.  Devices  to  keep  the  gasket 
from  being  blown  out,  such  as  a  circular  depression  in  one  flange 
in  which  the  gasket  is  placed  and  compressed  by  means  of  a  cor- 


[  FIG.  63. 

responding  projection  on  the  mating  flange,  are  not  mentioned  in 
the  specifications  of  the  American  Standard.  They  are,  however, 
much  used  in  high  pressure  work. 

The  screwed  joint  between  the  pipe  and  flange,  while  the  most 
common,  is  not  satisfactorily  effective  under  high  pressures. 
Numerous  methods  have  been  devised  to  improve  it.  The  one 
which,  for  cast  flanges,  seems  to  have  proved  most  generally 
satisfactory  is  shown  in  Fig.  63.  The  pipe  is  passed  entirely 
through  the  flange  and  the  end  afterward  expanded  to  form  a 
flange  of  its  own.  It  is  this  latter  flange  which  is  faced  true  to 
form  the  seat  for  the  gasket.  The  cast  iron  flanges  serve  as  bolting 
rings  to  draw  the  sections  of  pipe  together.  Flanges  made  of  steel 
may  be  welded  to  the  ends  of  the  pipe,  but  this  method  is  propor- 
tionately more  expensive.  Any  of  these  methods  are  open  to  the 
objection  that  the  faces  must  be  machined  after  the  flange  is  on. 
They  cannot,  therefore,  be  used  in  many  places  where  machinery 
is  not  available.  This  objection  is  not  very  serious  since,  for  the 


PIPE  AND  PIPE  FITTINGS 


85 


TABLE   XVIII. 
AMERICAN  STANDARD  PIPE  FLANGES. 


Standard  —  125  Lbs.  Pressure. 

Extra  Heavy  —  250  Lbs.  Pressure. 

Flange. 

Bolts. 

Flange. 

Bolts. 

Diameter. 

Diameter. 

4 

• 

4 

. 

£ 

3 

0 

4) 
G 

3 

.s 

1 

I 

0 

c 

1 

1 

3 

3 

o 

1 

IS 
H 

G 

OS 

Q'*"* 

a 
0 

"6 
m 

$ 

B 

c 

D 

B 

c 

D 

* 

1 

4 

3 

T6 

4 

A 

41 

31 

ii 

4 

1 

11 

41 

3f 

1 

4 

ft 

5 

3| 

f 

4 

U 

5 

31 

^ 

4 

6 

if 

4 

j 

2 

6 

4f 

| 

4 

i 

8| 

52 

1 

4 

•' 

2| 

7 

5| 

H 

4 

f 

51 

1 

4 

! 

3 

74 

6 

3 

4 

4 

f 

81 

6f 

H 

8 

3£ 

7 

jf 

4 

9 

71 

1ft 

8 

4 

92 

7| 

I 

8 

1 

10 

71 

H 

8 

4* 

91 

7f 

i 

8 

1 

lOf 

85 

1ft 

8 

5 

10 

81 

"I 

8 

f 

11 

91 

If 

8 

6 

11 

91 

1 

8 

a 

12| 

10f 

12 

! 

7 

12£ 

lOf 

1ft 

8 

| 

14 

HI 

12 

? 
i 

8 

13| 

Hf 

li 

8 

15 

13 

12 

j 

8 

9 

15 

131 

H 

12 

4~ 

161 

14 

12 

1 

10 

16 

141 

ift 

12. 

7 
8 

17* 

151 

H 

16 

1 

12 

19 

17 

12 

1 

20^ 

17f 

2 

16 

li 

14 

21 

18f 

12 

1 

23 

201 

2i 

20 

U 

15 

221 

20 

16 

1 

24^ 

21? 

2j^ 

20 

A  4 

16 

23^ 

211 

16 

1 

25£ 

21 

20 

18 

25 

221 

TS 

16 

li 

28 

24| 

2| 

24 

ii 

20 

27| 

25 

20 

li 

30^ 

27 

2| 

24 

ij 

22 

29| 

271 

20 

11 

33 

291 

2f 

24 

24 

32 

29^ 

20 

11 

36 

32 

2| 

24 

ij 

26 

341 

31f 

2 

24 

H 

381 

34^ 

28 

if 

28 

34 

2rir 

28 

H 

40f 

37 

2if 

28 

n 

30 

38f 

36 

2i 

28 

if 

43 

391 

3 

28 

H 

32 

41| 

38£ 

21 

28 

451 

41| 

3i 

28 

11 

34 

43f 

40^ 

2^ 

32 

if 

47^ 

31 

28 

11 

36 

46 

42f 

2| 

32 

U 

50 

46  2 

3f 

32 

u 

38 

481 

451 

2| 

32 

if 

521 

48 

3^ 

32 

H 

40 

50| 

471 

2i 

36 

if 

541 

501 

3JL 

36 

if 

42 

53 

2f 

36 

if 

57 

521 

3ft 

36 

H 

44 

551 

511 

2f 

40 

if 

591 

55 

3f 

36 

2 

46 

48 

571 

P\Qi 

56 

2H 
2| 

40 

44 

l| 

if 

65  2 

571 
601 

31 
4 

40 
40 

2 

2 

86  PIPE  AND  PIPE  FITTINGS 

best  results,  the  screwed  flange  should  also  be  trued  up  after  it  is 
on.  Except  on  large  contracts,  where  it  would  pay  to  set  up  the 
necessary  machinery  on  the  job,  it  is  advisable  to  have  the  pipe 
cut  to  lengths  and  all  flanges  put  on  and  faced  true  at  the  mill. 
52.  Pipe  Bends. — Besides  the  straight  section,  pipe  in  sizes 
up  to  24"  may  be  obtained  curved  to  various  forms  such  as  those 
shown  in  Fig.  64.  The  curved  portions  are  bent  to  the  arc  of  a 
circle  but  short  straight  portions  at  the  ends  are  necessary  in  mak- 


Expansion  U  Bend. 


Double  Offset  U  Bend. 


FIG.  64. 


ing  the  bends.  The  recommended  values  for  the  radii  of  the  curved 
portions  and  the  necessary  lengths  for  the  straight  ends  are  given 
in  Table  XIX.  By  using  extra  strong  pipe  these  radii  may  be 
reduced  to  the  minimum  values  given  in  the  table  but  the  makers 
do  not  guarantee  such  bends  against  buckling.  Pipe  bends  are 
usually  made  to  order.  The  distance  between  the  flange  faces  and 
the  amount  of  the  offset  in  the  offset  bend,  Fig.  64  (c),  and  the 
amount  of  the  offset  in  the  double  offset  U  bend,  Fig.  64 (e),  are 
optional  within  certain  limits.  Straight  portions  of  limited  length 
may  usually  be  added  where  desired  in  any  of  the  forms.  In  all 
cases  pipe  bends  are  furnished  with  the  flanges  on  and  faced  true 
to  the  desired  angle. 


PIPE  AND  PIPE   FjTTtNGS. 


87 


TABLE  XIX. 
PROPORTIONS  FOR  PIPE  BENDS. 


Radius  of  Bend. 

Radius  of  Bend. 

1 

'      1 

' 

fH 

^ 

w 

s 

"2 

fa 

a 

•a 

03 

| 

.c 

M 

q 

T3 

6 

M 

•g 

a 

03 

c 

ca 

IM 

0 

c 

a 

3 

2 

s 

Cfi 

s 

35 

| 

w 

^ 

S 

a 

R 

R 

s 

R 

R 

s 

21 

121 

7 

4 

10 

50 

40 

12 

3 

15 

8 

4 

12 

60 

50 

14 

171 

10 

5 

14 

70 

65 

16 

4 

20 

12 

5 

15 

75 

70 

16 

4* 

22^ 

14 

6 

16 

80 

78 

18 

5 

25 

15 

6 

18 

108 

88 

18 

6 

30 

20 

7 

20 

120 

104 

18 

7 

35 

24 

8 

22 

132 

132 

18 

8 

40 

28 

9 

24 

144 

144 

18 

9 

45 

35 

11     * 

53.  Pipe  Fittings. — The  forms  of  pipe  fittings  are  too  numerous 
for  complete  description  or  illustration  in  this  book.  They  are 
usually  of  cast  iron  but  steel  or  bronze  castings  may  be  required 
for  special  work.  Their  flanges  conform  to  the  specifications  given 
for  pipe  flanges  in  article  51.  The  finished  center  to  face  or  face 
to  face  distances  and  the  minimum  thicknesses  of  body  metal  in 
standard  fittings  for  sizes  of  pipe  up  to  48"  are  given  in  Tables  XX 
and  XXI  and  corresponding  values  for  extra  heavy  fittings  are 
given  in  Tables  XXII  and  XXIII.  The  symbols  apply  to  the  key 
drawings,  Fig.  65  on  page  92,  which  illustrate  some  of  the  more 
common  fornio.  The  nominal  size  of  pipe  is  that  corresponding 
to  the  largest  opening  in  the  fitting. 

The  direct  passage  through  a  fitting  is  known  as  the  run.  The 
side  openings  are  called  branches.  When  these  openings  are  of 
different  sizes  those  of  the  run  are  given  first  and  followed  by  those 
of  the  branches.  Tees,  crosses  and  laterals  are  made  in  two 
lengths  of  run,  known  respectively  as  shoit  body  and  long  body 
patterns.  The  short  body  is  used  only  when  the  diameter  of  the 
largest  branch  is  considerably  less  than  (approximately  two-thirds 
in  tees  and  crosses  and  one-half  in  laterals)  that  of  the  run,  in 
sizes  of  pipe  18"  or  larger.  The  maximum  diameter  of  branch 
for  the  short  body  pattern  and  the  minimum  outlets  for  these 
fittings  are  given  in  the  tables. 


88 


PIPE  AND  PIPE  FITTINGS 


TABLE  XX. 
AMERICAN  STANDARD  FLANGED  FITTINGS. 


Tees,  Crosses  and  Elbows.     Standard  Weight  —  125  Ibs.  Pressure. 

«-  G 

Distance  Center  to  Face. 

"o 

II 

« 

Tees  and  Crosses 

Elbows. 

4> 

§* 

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o 

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2 

PIPE  AND  PIPE  FITTINGS 

TABLE   XXI. 
AMERICAN  STANDARD  FLANGED  FITTINGS. 


89 


Laterals  and  Reducers.     Standard  Weight—  125  Lbs.  Pressure. 

Distance  Center  to  Face. 

Face  to  Face. 

'o 

o  £ 

Laterals. 

Laterals. 

1 

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90 


PIPE  AND  PIPE  FITTINES 


TABLE  XXII. 
AMERICAN  STANDARD  FLANGED  FITTINGS. 


Tees,  Crosses  and  Elbows.     Extra  Heavy  —  250  Ibs.  Pressure. 

•§  * 

Distance  Center  to  Face. 

o 

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Elbows. 

rt  as 

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PIPE  AND  PIPE  FITTINGS 


91 


TABLE  XXIII. 
AMERICAN  STANDARD  FLANGED  FITTINGS. 


Laterals  and  Reducers.     Extra  Heavy  —  250  Lbs.  Pressure 

Distance  Center  to  Face 

Face  to  Face. 

si 

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Laterals. 

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3 

PIPE  AND  PIPE  FITTINGS 


Tee. 


Reducing  Cross, 
(Short  Body) 

to 


UJ 


Long  Radius  Elbow. 

w 


so 


3.JL 


45°  Elbow. 
(f) 


Reducing  Lateral. 
(Short  Body) 

(A) 

FIG.  65. 


Reducer. 
(0 


54.  Valves  — Valves  for  the  purpose  of  shutting  off  the  flow 
of  fluid  through  a  pipe  are  made  in  two  general  types,  namely, 
globe  valves  and  gate  valves.  These  two  types  are  shown  in  sec- 
tion in  Figs.  66(a)  and  66(b)  respectively.  The  gate  valve  is  for 
some  purposes  preferred  to  the  globe  valve  because  of  the  more 


PIPE  AND  PIPE  FITTINGS 


93 


direct  passage  of  the  fluid  when  the  valve  is  open.     Many  other 
forms  of  valves  are  made  for  special  purposes.     The  openings  of 

' 


PIG.  66. 


the  valve  may  be  threaded  and  the  pipe  screwed  in  or  they  may  be 
flanged.  The  flanges  on  valves  are  made  to  conform  to  the 
specifications  given  in  article  51  on  page  82. 


DECIMAL  EQUIVALENTS  OF  FRACTIONS  OF  ONE  INCH. 


o5 
I 

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1 

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95 


96 


NATURAL  TRIGONOMETRIC  FUNCTIONS 


I 

SINES 

CO 

6 

H 

.3 

P 

0' 

10' 

20' 

30' 

40' 

50' 

60' 

0 

0 

0.00000 

0.00291 

0.00582 

0.00873 

0.01164 

0.01454 

0.01745 

89 

1 

0.01745 

0.02036 

0.02327 

0.02618 

0.02908 

0.03199 

0.03490 

88 

2 

0.03490 

0.03781 

0.04071 

0.04362 

0.04653 

0.04943 

0.05234 

87 

3 

0.05234 

0.05524 

0.05814 

0.06105 

0.06395 

0.06685 

0.06976 

86 

4 

0.06976 

0.07266 

0.07556 

0.07846 

0.08136 

0.08426 

0.08716 

85 

5 

0.08716 

0.09005 

0.09295 

0.09585 

0.09874 

0.10164 

0.10453 

84 

6 

0.10453 

0.10742 

0.11031 

0.11320 

0.11609 

0.11898 

0.12187 

83 

7 

0.12187 

0.12476 

0.12764 

0.13053 

0.13341 

0.13629 

0.13917 

82 

8 

0.13917 

0.14205 

0.14493 

0.14781 

0.15069 

0.15356 

0.15643 

81 

9 

0.15643 

0.15931 

0.16218 

0.16505 

0.16792 

0.17078 

0.17365 

80 

10 

0.17365 

0.17651 

0.17937 

0.18224 

0.18509 

0.18795 

0.19081 

79 

11 

0.19081 

0.19366 

0.19652 

0.19937 

0.20222 

0.20507 

0.20791 

78 

12 

0.20791 

0.21076 

0.21360 

0.21644 

0.21928 

0.22212 

0.22495 

77 

13 

0.22495 

0.22778 

0.23062 

0.23345 

0.23627 

0.23910 

0.24192 

76 

14 

0.24192 

0.24474 

0.24756 

0.25038 

0.25320 

0.25601 

0.25882 

75 

15 

0.25882 

0.26163 

0.26443 

0.26724 

0.27004 

0.27284 

0.27564 

74 

16 

0.27564 

0.27843 

0.28123 

0.28402 

0.28680 

0.28959 

0.29237 

73 

17 

0.29237 

0.29515 

0.29793 

0.30071 

0.30348 

0.30625 

0.30902 

72 

18 

0.30902 

0.31178 

0.31454 

0.31730 

0.32006 

0.32282 

0.32557 

71 

19 

0.32557 

0.32832 

0.33106 

0.33381 

0.33655 

0.33929 

0.34202 

70 

20 

0.34202 

0.34475 

0.34748 

0.35021 

0.35293 

0.35565 

0.35837 

69 

21 

0.35837 

0.36108 

0.36379 

0.36650 

0.36921 

0.37191 

0.37461 

68 

22 

0.37461 

0.37730 

0.37999 

0.38268 

0.38537 

0.38805 

0.39073 

67 

23 

0.39073 

0.39341 

0.39608 

0.39875 

0.40142 

0.40408 

0.40674 

66 

24 

0.40674 

0.40939 

0.41204 

0.41469 

0.41734 

0.41998 

0.42262 

65 

25 

0.42262 

0.42525 

0.42788 

0.43051 

0.43313 

0.43575 

0.43837 

64 

26 

0.43837 

0.44098 

0.44359 

0.44620 

0.44880 

0.45140 

0.45399 

63 

27  ' 

0.45399 

0.45658 

0.45917 

0.46175 

0.46433 

0.46690 

0.46947 

62 

28 

0.46947 

0.47204 

0.47460 

0.47716 

0.47971 

0.48226 

0.48481 

61 

29 

0.48481 

0.48735 

0.48989 

0.49242 

0.49495 

0.49748 

0.50000 

60 

30 

0.50000 

0.50252 

0.50503 

0.50754 

0.51004 

0.51254 

0.51504 

59 

31. 

0.51504 

0.51753 

0.52002 

0.52250 

0.52498 

0.52745 

0.52992 

58 

32 

0.52992 

0.53238 

0.53484 

0.53730 

0.53975 

0.54220 

0.54464 

57 

33 

0.54464 

0.54708 

0.54951 

0.55194 

0.55436 

0.55678 

0.55919 

56 

34 

0.55919 

0.56160 

0.56401 

0.56641 

0.56880 

0.57119 

0.57358 

55 

35 

0.57358 

0.57596 

0.57833 

0.58070 

0.58307 

0.58543 

0.58779 

54 

36 

0.58779 

0.59014 

0.59248 

0.59482 

0.59716 

0.59949 

0.60182 

53 

37 

0.60182 

0.60414 

0.60645 

0.60876 

0.61107 

0.61337 

0.61566 

52 

38 

0.61566 

0.61795 

0.62024 

0.62251 

0.62479 

0.62706 

0.62932 

51 

39 

0.62932 

0.63158 

0.63383 

0.63608 

0.63832 

0.64056 

0.64279 

50 

40 

0.64279 

0.64501 

0.64723 

0.64945 

0.65166 

0.65386 

0.65606 

49 

41 

0.65606 

0.65825 

0.66044 

0.66262 

0.66480 

0.66697 

0.66913 

48 

42 

0.66913 

0.67129 

0.67344 

0.67559 

0.67773 

0.67987 

0.68200 

47 

43 

0.68200 

0.68412 

0.68624 

0.68835 

0.69046 

0.69256 

0.69466 

46 

44 

0.69466 

0.69675 

0.69883 

0.70091 

0.70298 

0.70505 

0.70711 

45 

60' 

50' 

40' 

30' 

20' 

10' 

0' 

CO 

1 

CD 

1 

COSINES 

Q 

NATURAL  TRIGONOMETRIC  FUNCTIONS 


97 


CO 

a 

COSINES 

CO 

p 

I 

0' 

10' 

20' 

30' 

40' 

50' 

60' 

0 

1.00000 

1.00000 

0.99998 

0.99996 

0.99993 

0.99989 

0.99985 

89 

1 

0.99985 

0.99979 

0.99973 

0.99966 

0.99958 

0.99949 

0.99939 

88 

2 

0.99939 

0.99929 

0.99917 

0.99905 

0.99892 

0.99878 

0.99863 

87 

3 

0.99863 

0.99847 

0.99831 

0.99813 

0.99795 

0.99776 

0.99756 

86 

4 

0.99756 

0.99736 

0.99714 

0.99692 

0.99668 

0.99644 

0.99619 

85 

5 

0.99619 

0.99594 

0.99567 

0.99540 

0.99511 

0.99482 

0.99452 

84 

6 

0.99452 

0.99421 

0.99390 

0.99357 

0.99324 

0.99290 

0.99255 

83 

7 

0.99255 

0.99219 

0.99182 

0.99144 

0.99106 

0.99067 

0.99027 

82 

8 

0.99027 

0.98986 

0.98944 

0.98902 

0.98858 

0.98814 

0.98769 

81 

9 

0.98769 

0.98723 

0.98676 

0.98629 

0.98580 

0.98531 

0.98481 

8Q 

10 

0.98481 

0.98430 

0.98378 

0.98325 

0.98272 

0.98218 

0.98163 

79 

11 

0.98163 

0.98107 

0.98050 

0.97992 

0.97934 

0.97875 

0.97815 

78 

12 

0.97815 

0.97754 

0.97692 

0.97630 

0.97566 

0.97502 

0.97437 

77 

13 

0.97437 

0.97371 

0.97304 

0.97237 

0.97169 

0.97100 

0.97030 

76 

14 

0.97030 

0.96959 

0.96887 

0.96815 

0.96742 

0.96667 

0.96593 

75 

15 

0.96593 

0.96517 

0.96440 

0.96363 

0.96285 

0.96206 

0.96126 

74 

16 

0.96126 

0.96046 

0.95964 

0.95882 

0.95799 

0.95715 

0.95830 

73 

17 

0.95630 

0.95545 

0.95459 

0.95372 

0.95284 

0.95195 

0.95106 

72 

18 

0.95106 

0.95015 

0.94924 

0.94832 

0.94740 

0.94646 

0.94552 

71 

19 

0.94552 

0.94457 

0.94361 

0.94264 

0.94167 

0.94068 

0.93969 

70 

20 

0.93969 

0.93869 

0.93769 

0.93667 

0.93565 

0.93462 

0.93358 

69 

21 

0.93358 

0.93253 

0.93148 

0.93042 

0.92935 

0.92827 

0.92718 

68 

20 

0.92718 

0.92609 

0.92499 

0.92388 

0.92276 

0.92164 

0.92050 

67 

23 

0.92050 

0.91936 

0.91822 

0.91706 

0.91590 

0.91472 

0.91355 

66 

24 

0.91355 

0.91236 

0.91116 

0  90996 

0.90875 

0.90753 

0.90631 

65 

25 

0.90631 

0.90507 

0.90383 

0.90259 

0.90133 

0.90007 

0.89879 

64 

26 

0.89879 

0.89752 

0.89623 

0.89493 

0.89363 

0.89232 

0.89101 

63 

27 

0.89101 

0.88968 

0.88835 

0.88701 

0.88566 

0.88431 

0.88295 

62 

28 

0.88295 

0.88158 

0.88020 

0.87882 

0.87743 

0.87603 

0.87462 

61 

29 

0.87462 

0.87321 

0.87178 

0.87036 

0.86892 

0.86748 

0.86603 

60 

30 

0.86603 

0.86457 

0.86310 

0.86163 

0.86015 

0.85866 

0.85717 

59 

31 

0.85717 

0.85567 

0.85416 

0.85264 

0.85112 

0.84959 

0.84805 

58 

32 

0.84805 

0.84650 

0.84495 

0.84339 

0.84182 

0.84025 

0.83867 

57 

33 

0.83867 

0.83708 

0.83549 

0.83389 

0.83228 

0.83066 

0.82904 

56 

34 

0.82904 

0.82741 

0.82577 

0.82413 

0.82248 

0.82082 

0.81915 

55 

35 

0.81915 

0.81748 

0.81580 

0.81412 

0.81242 

0.81072 

0.80902 

54 

36 

0.80902 

0.80730 

0.80558 

0.803S6 

0.80212 

0.80038 

0.79864 

53 

37 

0.79863 

0.79688 

0.79512 

0.79335 

0.79158 

0.78980 

0.78801 

52 

38 

0.78801 

0.78622 

0.78442 

0.78261 

0.78079 

0.77897 

0.77715 

51 

39 

0.77715 

0.77531 

0.77347 

0.77162 

0.76977  • 

0.76791 

0.76604 

50 

40 

0.76604 

0.76417 

0.76229 

0.76041 

0,75851 

0.75661 

0.75471 

49 

41 

0.75471 

0.75280 

0.75038 

0.74896 

0.74703 

0.74509 

0.74314 

48 

42 

0.74314 

0.74120 

0.73924 

0.73728 

0.73531 

0.73333 

0.73135 

47 

43 

0.73135 

0.72937 

0.72737 

0.72537 

0.72337 

0.72136 

0.71934 

46 

44 

0.71934 

0.71732 

0.71529 

0.71325 

0.71121 

0.70916 

0.70711 

45 

CO 
0) 

.3 

60' 

50' 

40' 

30' 

20' 

10' 

0' 

I 

fli 

J 

SINES 

1 
Q 

98 


NATURAL  TRIGONOMETRIC  FUNCTIONS 


I 

TANGENTS 

| 

Q 

0' 

10' 

20' 

30' 

40' 

50' 

60' 

1 

0 

O 

0 

0.00000 

0.00291 

0.00582 

0.00873 

0.01164 

0.01455 

0.01746 

89 

1 

0.01746 

0.02036 

0.02328 

0.02619 

0.02910 

0.03201 

0.03492 

88 

2 

0.03492 

0.03783 

0.04075 

0.04366 

0.04658 

0.04949 

0.05241 

87 

3 

0.05241 

0.05533 

0.05824 

0.06116 

0.06408 

0.06700 

0.06993 

86 

4 

0.06993 

0.07285 

0.07578 

0.07870 

0.08163 

0.08456 

0.08749 

85 

5 

0.08749 

0.09042 

0.09335 

0.09629 

0.09923 

0.10216 

0.10510 

84 

6 

0.10510 

0.10805 

0.11099 

0.11394 

0.11688 

0.11983 

0.12278 

83 

7 

0.12278 

0.12574 

0.12869 

0.13165 

0.13461 

0.13758 

0.14054 

82 

8 

0.14054 

0.14351 

0.14648 

0.14945 

0.15243 

0.15540 

0.15838 

81 

9 

0.15838 

0.16137 

0.16435 

0.16734 

0.17033 

0.17333 

0.17633 

80 

id 

0.17633 

0.17933 

0.18233 

0.18534 

0.18835 

0.19136 

0.19438 

79 

11 

0.19438 

0.19740 

0.20042 

0.20345 

0.20648 

0.20952 

0.21256 

78 

12 

0.21256 

0.21560 

0.21864 

0.22169 

0.22475 

0.22781 

0.23087 

77 

13 

0.23087 

0.23393 

0.23700 

0.24008 

0.24316 

0.24624 

0,24933 

76 

14 

0.24933 

0.25242 

0.25552 

0.25862 

0.26172 

0.26483 

0.26795 

75 

15 

0.26795 

0.27107 

0.27419 

0.27732 

0.28046 

0.28260 

0.28675 

74 

16 

0.28675 

0.28990 

0.29305 

0.29621 

0.29938 

0.30255 

0.30573 

73 

17 

0.30573 

0.30891 

0.31210 

0.31530 

0.31850 

0.32171 

0.32492 

72 

18 

0.32492 

0.32814 

0.33136 

0.33460 

0.33783 

0.34108 

0.34433 

71 

19 

0.34433 

0.34758 

0.35085 

0.35412 

0.35740 

0.36068 

0.36397 

70 

20 

0.36397 

0.36727 

0.37057 

0.37388 

0.37720 

0.38053 

0.38386 

69 

21 

0.38386 

0.38721 

0.39055 

0.39391 

0.39727 

0.40065 

0.40403 

68 

22 

0.40403 

0.40741 

0.41081 

0.41421 

0.41763 

0.42105 

0.42447 

67 

23 

0.42447 

0.42791 

0.43136 

0.43481 

0.43S28 

0.44175 

0.44523 

66 

24 

0.44523 

0.44872 

0.45222 

0.45573 

0.45924 

0.46277 

0.46631 

65 

25 

0.46631 

0.46985 

0.47341 

0.47698 

0.48055 

0.48414 

0.48773 

64 

26 

0.48773 

0.49134 

0.49495 

0.49858 

0.50222 

0.50587 

0.50953 

63 

27 

0.50953 

0.51320 

0.51688 

0.52057 

0.52427 

0.52798 

0.53171 

62 

28 

0.53171 

0.53545 

0.53920 

0.54296 

0.54674 

0.55051 

0.55431 

61 

29 

0.55431 

0.55812 

0.56194 

0.56577 

0.56962 

0.57348 

0.57735 

60 

30 

0.57735 

0.58124 

0.58513 

0.58905 

0.59297 

0.59691 

0.60086 

59 

31 

0.60086 

0.60483 

0.60881 

0.61280 

0.61681 

0.62083 

0.62487 

58 

32 

0.62487 

0.62892 

0.63299 

0.63707 

0.64117 

0.64528 

0.64941 

57 

33 

0.64941 

0.65355 

0.65771 

0.66189 

0.66608 

0.67028 

0.67451 

56 

34 

0.67451 

0.67875 

0.68301 

0.68728 

0.69157 

0.69588 

0.70021 

55 

35 

0.70021 

0.70455 

0.70891 

0.71329 

0.71769 

0.72211 

0.72654 

54 

36 

0.72654 

0.73100 

0.73547 

0.73996 

0.74447 

0.74900 

0.75355 

53 

37 

0.75355 

0.75812 

0.76272 

0.76733 

0.77196 

0.77661 

0.78129 

52 

38 

0.78129 

0.78598 

0.79070 

0.79544 

0.80020 

0.80498 

0.80978 

51 

39 

0.80978 

0.81461 

0.81946 

0.82434 

0.82923 

0.83415 

0.83910 

50 

40 

0.83910 

0.84407 

0.84906 

0.85408 

0.85912 

0.86419 

0.86929 

49 

41 

0.86929 

0.87441 

0.87955 

0.88473 

0.88992 

0.89515 

0.90040 

48 

42 

0.90040 

0.90569 

0.91999 

0.91633 

0.92170 

0.92709 

0.93252 

47 

43 

0.93252 

0.93797 

0.94345 

0.94896 

0.95451 

0.96008 

0.96569 

46 

44 

0.96569 

0.97133 

0.97700 

0.98270 

0.98843 

0.99420 

1.00000 

45 

£ 

60' 

50' 

40' 

30' 

20' 

10' 

0' 

* 

§ 

0> 

bfl 
ft 

& 

£ 

COTANGENTS 

Q 

NATURAL  TRIGONOMETRIC  FUNCTIONS 


8 

COTANGENTS 

§ 

9 

<D 

& 

Q 

0' 

10' 

20' 

30' 

40' 

50' 

60' 

J 

0 

oo 

343.77371 

171.88540 

114.58865 

85.93979 

68.75009 

57.28996 

89 

1 

57.28996 

49.10388 

42.96408 

38.18846 

34.36777 

31.24158 

28.63625 

88 

2 

28.63625 

26.43160 

24.54176 

22.90377 

21.47040 

20.20555 

19.08114 

87 

3 

19.08114 

18.07498 

17.16934 

16.34986 

15.60478 

14.92442 

14.30067 

86 

4 

14.30067 

13.72674 

13.19688 

12.70621 

12.25051 

11.82617 

11.43005 

85 

5 

11.43005 

11.05943 

10.71191 

10.38540 

10.07803 

9.78817 

9.51436 

84 

6 

9.51436 

9.25530 

9.00983 

8.77689 

8.55555 

8.34496 

8.14435 

83 

7 

8.14435 

7.95302 

7.77035 

7.59575 

7.42871 

7.26873 

7.11537 

82 

8 

7.11537 

6.96823 

6.82694 

6.69116 

6.56055 

6.43484 

6.31375 

81 

9 

6.31375 

6.19703 

6.08444 

5.97576 

5.87080 

5.76937 

5.67128 

80 

10 

5.67128 

5.57638 

5.48451 

5.39552 

5.30928 

5.22566 

5.14455 

79 

11 

5.14455 

5.06584 

4.98940 

4.91516 

4.84300 

4.77286 

4.70463 

78 

12 

4.70463 

4.63825 

4.57363 

4.51071 

4.44942 

4.38969 

4.33148 

77 

13 

4.33148 

4.27471 

4.21933 

4.16530 

4.11256 

4.06107 

4.01078 

76 

14 

4.01078 

3.96165 

3.91364 

3.86671 

3.82083 

3.77595 

3.73205 

75 

15 

3.73205 

3.68909 

3.64705 

3.60588 

3.56557 

3.52609 

3.48741 

74 

16 

3.48741 

3.44951 

3.41236 

3.37594 

3.34023 

3.30521 

3.27085 

73 

17 

3.27085 

3.23714 

3.20406 

3.17159 

3.13972 

3.10842 

3.07768 

72 

18 

3.07768 

3.04749 

3.01783 

2.98869 

2.96004 

2.93189 

2.90421 

71 

19 

2.90421 

2.87700 

2.85023 

2.82391 

2.79802 

2.77254 

2.74748 

70 

20 

2.74748 

2.72281 

2.69853 

2.67462 

2.65109 

2.62791 

2.60509 

69 

21 

2.60509 

2.58261 

2.56046 

2.53865 

2.51715 

2.49597 

2.47509 

68 

22 

2.47509 

2.45451 

2.43422 

2.41421 

2.39449 

2.37504 

2.35585 

67 

23 

2.35585 

2.33693 

2.31826 

2.29984 

2.28176 

2.26374 

2.24604 

66 

24 

2.24604 

2.22857 

2.21132 

2.19430 

2.17749 

2.16090 

2.14451 

65 

25 

2.14451 

2.12832 

2.11233 

2.09654 

2.08094 

2.06553 

2.05030 

64 

26 

2.05030 

2.03526 

2.02039 

2.00569 

.99116 

.97680 

.96261 

63 

27 

.96261 

1.94858 

.93470 

.92098 

.90741 

.89400 

.88073 

62 

28 

.88073 

1.86760 

.85462 

.84177 

.82907 

.81649 

.80405 

61 

29 

.80405 

1.79174 

.77955 

.76749 

.75556 

.74375 

.73205 

60 

30 

.73205 

1.72047 

.70901 

.69766 

.68643 

.67530 

.66428 

59 

31 

.66428 

1.65337 

.64256 

.63185 

.62125 

.61074 

.60033 

58 

32 

.60033 

1.59002 

.56981 

1.56969 

.55966 

1.54972 

.53987 

57 

33 

.53987 

1.53010 

1.52043 

1.51084 

.50133 

1.49190 

.48256 

56 

34 

.48256 

1.47330 

1.46411 

1.45501 

.44598 

1.43703 

.42815 

55 

35 

1.42815 

1.41934 

1.41061 

1.40195 

1.39336 

1.38484 

.37638 

54 

36 

1.37638 

1,36800 

1.35968 

1.35142 

1.34323 

1.33511 

.32704 

53 

37 

1.32704 

1.31904 

1.31110 

1.30323 

1.29541 

1.28764 

.27994 

52 

38 

1.27994 

1.27230 

1.26471 

1.25717 

1.24969 

1.24227 

.23490 

51 

39 

1.23490 

1.22758 

1.22031 

1.21310 

1.20593 

1.19882 

.19175 

50 

40 

1.19175 

1.18474 

1.17777 

1.17085 

1.16398 

1.15715 

1.15037 

49 

41 

1.15037 

1.14363 

1.13694 

1.13029 

1.12369 

1.11713 

1.11061 

48 

42 

1.11061 

1.10414 

1.09770 

1.09131 

1.08496 

1.07684 

1.07237 

47 

43 

1.07237 

1.06613 

1.05994 

1.05378 

1.04766 

1.04158 

1.03553 

46 

44 

1.03553 

1.02952 

1.02355 

1.01761 

1.01170 

1.00583 

1.00000 

45 

9 

a 

ho 

60' 

50' 

40' 

30' 

20' 

10' 

0' 

09 

1 
r  -\ 

TANGENTS 

P 

INDEX 

Addendum,  definition  of,  68. 

Adjustments  of  bearings,  48. 

Anchorages  for  babbitt,  46. 

Automobile  bolts,  special  characteristics  of,  14. 

table  of  proportions  for,  16. 
Babbitted  bearings,  proportions  for,  49. 

methods  of  lining,  46. 
Base  plates,  use  of,  56. 
Bearings,  adjustments  of,  48. 

babbitted,  proportions  for,  49. 

methods  of  lining,  46. 
commercial  forms  of,  47. 
general  description  of,  46. 
materials  used  for,  46. 
methods  of  supporting,  48,  55. 
quarter-box,  description  and  use  of,  52. 

proportions  for,  55. 
step,  use  of,  47. 

Belting,  leather,  commercial  sizes  of,  65. 
Belts,  use  of  and  materials  for,  64. 
Bevel  gears,  pitch  surfaces  of,  68. 
proportions  for,  72. 
stock  sizes  of,  75. 

Bolts,  automobile,  special  characteristics  of,  15. 
table  of  proportions  for,  16. 
coupling,  description  and  stock  sizes  of,  14. 
hexagonal  heads  and  nuts  for,  use  of,  13. 
machine,  description  and  stock  sizes  of,  13. 
proportions  for  heads,  nuts  and  threads  for,  12,  14. 
stud,  description  and  stock  sizes  of,  15. 
table  of  dimensions  for,  14. 
tap,  description  and  stock  sizes  of,  15. 
use  of,  12. 
Boxes,  definition  of,  33. 

quarter,  description  and  use  of,  53. 
frames,  wall,  description  and  use  of,  58. 

proportions  for,  59. 
Brackets,  wall,  description  and  use  of,  56. 

proportions  for,  58. 
Cams,  disk,  proportions  for,  76. 

for  gas  engines,  proportions  for,  76. 
stamp  mill,  proportions  for,  77. 
Cap  screws,  description  and  stock  sizes  of,  20. 
Castellated  nuts,  description  and  use  of,  17. 

table  of  proportions  for,  16. 
Cast  iron  washers,  table  of,  19. 

use  of,  18. 

Circular  pitch,  definition  of,  68. 
Clutch  couplings,  description  of,  38. 
Clutches,  friction,  use  of,  42. 

jaw,  description  and  use  of,  38. 
proportions  for,  39. 
shifting  collar  for,  41. 
shifting  lever  for,  42. 


102  INDEX 


Collars  for  shafting,  proportions  for,  44. 

use  of,  43. 
shifting  for  jaw  clutches,  description  and  use  of,  40. 

proportions  for,  41. 

Compression  couplings,  definition  of,  35. 
Coupling  bolts,  description  and  stock  sizes  of,  14. 
Couplings,  clutch,  description  of,  38. 

compression,  definition  of,  35. 
flanged,  description  of,  36. 

proportions  for,  37. 
for  shafting,  requirements  for,  34. 
keyless,  description  of,  35. 
pipe,  description  and  stock  sizes  of,  82. 
sleeve,  description  of,  34. 
Cut  washers,  table  of  proportions  for,  19. 

use  of,  18. 

Decimal  equivalents  of  fractions  of  one  inch,  95. 
Diametral  pitch,  definition  of,  68 
Disk  cams,  proportions  for,  76. 
Edge  angle,  definition  of,  73. 
Empirical  design,  definition  of,  5. 

Empirical  equations,  determination  and  advantages  of,  8 . 
Empirical  methods,  application  to  standardized  machine  parts.  5 

use  of  in  modern  design,  5. 
Face  angle,  definition  of,  73. 
Feather  keys,  description  and  use  of,  28. 

tables  of  proportions  for,  28,  30. 
Flanges  couplings,  description  of,  36. 

proportions  for,  37. 
Flanged,  pipe,  description  and  forms  of,  82. 

table  of  dimensions  for,  85. 
Floor  stands,  use  of,  56. 
Fractions  of  an  inch,  decimal  equivalents  of,  95. 

'used  in  dimensions,  6. 
Friction  clutches,  use  of,  42. 
Gas  engine  cams,  proportions  for,  76. 
Gaskets,  definition  and  use  of,  82. 
Gears,  bevel,  proportions  for,  72. 
pitch  surfaces  of,  68. 
stock  sizes  of,  75. 
commercial  stock  sizes  of,  75. 
dimensioning  on  drawings  of,  69,  71. 
materials  used  for,  70. 
mitre,  definition  of,  68. 
stock  sizes  of,  75. 
mortise,  definition  of,  70. 
purpose  and  forms  of,  67. 
spur,  pitch  surfaces  for,  68. 
proportions  for,  70. 
stock  sizes  of,  75. 
worm,  pitch  surfaces  of,  68. 
proportions  for,  73. 
stock  sizes  of,  75. 

Gear  teeth,  proportions  and  properties  of,  68. 
Gib  keys,  description  and  use  of,  25. 
stock  sizes  of,  28. 


.     INDEX  103 

Graphical  determinations  in  empirical  design,  6. 
Hand  wheels,  empirical  design  of  bore  and  hub  for,  6. 

use  and  forms  of,  65. 

Hanger  screws,  description  and  stock  sizes  of,  24. 
Hangers,  shaft,  use  of,  60. 
Jam  nuts,  use  of  and  proportions  for,  17. 
Jaw  clutches,  description  and  use  of,  38. 
proportions  for,  39. 
shifting  collar  for,  41. 
shifting  lever  for,  42. 
Journal  boxes,  definition  of,  33. 
Journals,  definition  of,  33. 
Keys,  feather,  description  and  use  of,  28. 

tables  of  proportions  for,  28,  30. 
gib,  description  and  use  of,  25. 

stock  sizes  of,  28. 
special  proportions  for,  28. 
standard  forms  and  proportions  for,  25. 
straight,  use  of,  26. 
taper,  stock  sizes  of,  28. 

use  of,  27. 
use  of,  25. 

Woodruff  system  of,  29. 
Key  ways  or  key  seats,  definition  of,  25. 
in  shafting,  33. 

proportions  for  in  the  United  States,  31. 
Lag,  screws,  description  and  stock  sizes  of,  24. 
Leather  belting,  commercial  sizes  of,  65. 
Machine  bolts,  description  and  stock  sizes  of,  13. 
Machine  screws,  A.  S.  M.  E.  standard  for,  21. 

description  and  stock  sizes  of  21. 

Marine  nut,  locks,  description  of  and  proportions  for,  18. 
Mitre  gears,  definition  of,  68. 
stock  sizes  of,  75. 
Mortise  gears,  definition  of,  70. 
Nut  locks,  use  of,  17. 

marine,  description  of  and  proportions  for,  18. 
Nuts,  castellated,  description  and  use  of,  17. 

table  of  proportions  for,  16. 
jam,  use  of  and  proportions  for,  17. 
Pinion,  definition  of,  67. 
Pins,  taper,  description  and  stock  sizes  of,  31. 
Pipe,  varieties  of,  79. 

wrought  iron  and  steel,  commercial  sizes  and  weights  of,  79. 

table  of  dimensions  of,  80. 
Pipe  bends,  description  of,  86. 

table  of  dimensions  for,  87. 
couplings,  description  and  stock  sizes  of,  82. 
fittings,  flanged,  description  of,  87. 

tables  of  dimensions  for,  88,  89,  90,  91. 
flanges,  standards  for,  83. 

tables  of  dimensions  for,  85. 
joints,  general  types  of,  82. 
threads,  Briggs  standard,  proportions  of,  81. 
table  of,  80. 


104  INDEX 


Pitch,  diametral,  definition  of,  68. 
circular,  definition  of,  68. 
circle  or  pitch  line,  definition  of,  68. 
diameter,  definition  of,  68. 
surfaces,  definition  and  common  forms  ot,  67 
Pulleys,  commercial  sizes  of,  62. 

proportions  for,  63. 
Quarter-boxbearings,  description  and  use  of,  52. 

proportions  for,  55. 
Safety  collars,  proportions  for,  44. 
Screw  fastenings,  general  classes  of,  11. 

specifications  on  drawings,  1 1 . 
standardization  of,  11. 
use  of,  11,  19. 

Screws,  cap,  description  and  stock  sizes  of,  20. 
for  metal  use  of,  19. 
for  wood,  use  and  forms  of,  23. 
hanger,  description  and  stock  sizes  of,  24 . 
lag,  description  and  stock  sizes  of,  24. 
machine,  A.  S.  M.  E.  standard  for,  21. 

description  and  stock  sizes  of,  21. 
set,  description  and  stock  sizes  of,  22. 
use  of,  11,  19. 

wood,  description  and  stock  sizes  of,  24. 
Set  screws,  description  and  stock  sizes  of,  22. 
Shaft,  definition  of,  33. 

couplings,  requirements  for,  34. 
fixtures,  classification  of,  46.     * 
Shafting,  commercial  sizes  of,  33. 
Sleeve  couplings,  description  of,  34. 
Splines,  description  and  use  of,  28. 

tables  of  proportions  for,  28,  30. 
Spur  gears,  pitch  surfaces  for,  68. 
proportions  for,  70. 
stock  sizes  of,  75. 

Stamp  mill  cams,  proportions  for,  77. 

Standardized  machine  parts,  design  of  by  empirical  methods    5. 
Step  bearings,  use  of,  47. 
Straight  keys,  use  of,  26. 
Stud  bolts,  description  and  stock  sizes  of,  15. 
Studs,  description  and  stock  sizes  of,  15. 
Tap  bolts,  description  and  stock  sizes  of,  15. 
Taper  keys,  stock  sizes  of,  28. 

use  of,  27. 

Taper  pins,  description  and  stock  sizes  of,  31. 
Threads,    screw,  common  forms  of,  12. 

pipe,  Briggs  standard,  proportions  of,  81. 

table  of,  80. 
Trigonometric  functions,  natural,  96. 

United  States  standard  thread,  description  of,  12. 
Valves,  globe  and  gate,  description  of,  92. 

Wall  box  frames,  description  and  use  of,  58. 
proportions  for,  59. 


INDEX  105 


Washers,  cast  iron,  table  of  dimensions  for,  19. 

use  of,  18. 
wrought  iron  and  steel,  table  of  dimensions  for,  19. 

use  of,  18. 
Woodruff  system  of  keys,  description  of,  28. 

table  of  proportions  for,  29. 
Wall  brackets,  description  and  use  of,  56. 

proportions  for,  58. 

Wood  screws,  description  and  stock  sizes  of,  24. 
Worm  gears,  pitch  surfaces  of,  68. 
proportions  for,  73. 
stock  sizes  of,  75. 


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